Performance Evaluation of a Planar 3DOF Robotic ... - CiteSeerX

Stephen J. Ball Department of Electrical and Computer Engineering, Queen’s University, Kingston, ON, K7L 3N6, Canada e-mail: [email protected]

Ian E. Brown Department of Anatomy and Cell Biology, Centre for Neuroscience Studies, Queen’s University, Kingston, ON, K7L 3N6, Canada e-mail: [email protected]

Stephen H. Scott1 Department of Anatomy and Cell Biology, and Department of Medicine, Centre for Neuroscience Studies, Queen’s University, Kingston, ON, K7L 3N6, Canada e-mail: [email protected]

1

Performance Evaluation of a Planar 3DOF Robotic Exoskeleton for Motor Assessment A new planar robotic exoskeleton for upper-limb motor assessment has been developed. It provides independent control of a user’s shoulder, elbow, and wrist joints in the horizontal plane. The lightweight backdriveable robot is based on a novel cable-driven curved track and carriage system that enables the entire mechanism to be located underneath the user’s arm. It has been designed to extend the assessment capabilities of an existing planar robotic exoskeleton. This paper presents the design and performance of the new robot. 关DOI: 10.1115/1.3131727兴

Introduction

Robotic technology is becoming an important tool for quantifying and manipulating sensorimotor performance 关1–4兴. Robots have the ability to provide sensitive and inherently objective quantitative assessments of both the kinematics and the kinetics of movement. Moreover, robots excel at making repetitive controlled movements, and they are easy to incorporate into virtual reality environments. Not only does this have value in basic research of sensorimotor performance as a whole, but robotics is also being used as a tool for assessing and treating motor impairments 关5,6兴. Robots designed for the human upper-limb are differentiated primarily by the means of interfacing with the human and as such, they can be classified into one of two categories. End-point type robots 共sometimes called hand-held type兲 are devices in which the user grasps the end-effector of the robot using a handle or other attachment. Some examples include the MIT-Manus 关7兴 共now known as InMotion2 by Interactive Motion Technologies, Inc., Cambridge, MA兲 and MIME 关8兴, both of which are intended to provide movement training for stroke patients. The end-effector of the robot is the only point of attachment between the user and the robot, and is used to track the position of the user’s hand and also to apply forces. These robots are simple and versatile, and can easily be used for both planar and three-dimensional movements. However, the robot knows only about the hand kinematics, so it is not possible to quantify the individual joint kinematics of the limb. Moreover, torques cannot be applied directly to the joints of the user’s limb. Exoskeleton robots make up the second category. An exoskeleton robot is designed to align its joints with the joints of the user’s limb, allowing the distinct ability to monitor and control limb joints independently. Examples of this type of robot include T-WREX 关9兴 共now known as Armeo® by Hocoma, Volketswil, Switzerland兲, ARMin II 关10兴, and KINARM™ 关11兴 共BKIN Technologies Ltd., Kingston, ON, Canada兲. These robots must be attached to the user’s limb at multiple points, and they must be adjustable to accommodate users of different size. As a result of 1 Corresponding author. Manuscript received November 13, 2008; final manuscript received April 4, 2009; published online May 27, 2009. Review conducted by Vijay Goel. Paper presented at the 2007 IEEE International Conference on Engineering in Medicine and Biology Society.

Journal of Medical Devices

this close interaction with the user, exoskeleton robots tend to be more complex, and thus more expensive. Nevertheless, exoskeleton robots can provide substantial insight into the mechanics of limb motion and therefore are particularly well-suited to motor assessment. The existing KINARM robotic design permits analysis of planar limb movements involving flexion and extension movements of the shoulder and elbow joints and has been essential for uncovering many novel features of motor function in humans 关3,12–14兴 and in nonhuman primates 关15–17兴. However, there are several questions that it cannot address. In particular, the present design cannot address questions related to motor redundancy since the spatial and motor degrees of freedom are identical. The addition of a third joint at the wrist would allow subjects to make a reaching movement using a combination of three joints. Moreover, the addition of a third mechanical degree of freedom at the wrist also has practical value for quantifying sensorimotor impairments in stroke subjects. It is known that there is a proximodistal gradient in motor impairments following stroke with greater deficits tending to occur at more distal joints 关18–20兴. The addition of the wrist joint would greatly improve the ability of the KINARM robotic system to quantify this variation in motor impairments along the limb. KINARM is driven by equipment placed vertically along the shoulder joint axis, but above the shoulder because the torso prevents equipment from being placed underneath. The mechanism then extends around the arm to provide support for the limb from the underside. A consequence of this design is that the equipment must be placed beside the user’s head, which can cause users to feel claustrophobic in the system. Also, this design restricts access to the limb for clinicians. Therefore, in terms of user comfort and clinical appeal, it would be desirable to move all equipment underneath the arm. More importantly, however, the current design does not work in bilateral situations in which the distance between shoulders is small because there is not enough physical space for both exoskeletons. This problem is particularly apparent when studying upper-limb motion of children. In this context, it would be beneficial to move all of the equipment away from the user’s head so that there is no interference. With these ideas in mind, it was decided to build a new exoskeleton robot that could serve as a possible revision to KINARM. The design of this new device, called Planar MEDARM™, has

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been introduced previously 关21兴. The present paper describes the design of Planar MEDARM in more detail and discusses the performance of this new robot.

2

Design Objectives

The fundamental goal for Planar MEDARM is to develop a new exoskeleton design that can be used to study 3DOF planar limb movements versus the 2DOF available with KINARM. Adding this third DOF will permit both the measurement of motion at and the application of loads to the shoulder, elbow, and wrist in the horizontal plane. Secondary goals for Planar MEDARM are to avoid placing equipment beside head as per the present KINARM mechanism and to improve vertical out-of-plane compliance. These goals should be achieved without a significant compromise in performance relative to KINARM. Planar MEDARM should also be able to perform the same types of assessment tasks for which KINARM was designed. First of all, Planar MEDARM must be able to actuate each joint independently to permit application of a variety of joint-based loads. For example, this capability allows the robot to quantify the ability of a subject to compensate for perturbations applied to a joint during a whole-arm task 关14兴. In order to probe other aspects of limb motor performance, Planar MEDARM must be able to impose other more complex force fields, including stable viscous loads, on the subject’s limb during motion. The second and more challenging design feature is to minimize the influence of Planar MEDARM on natural limb movements. Therefore, the system should be backdriveable, and the friction should be as low as possible. Moreover, the inertia of the exoskeleton should be low and proportional to the upper-limb itself so that the user can adapt more easily when moving with the device. For all assessment tests, it is important that Planar MEDARM provides an accurate measure of the actual limb position. Any compliance in the robot will introduce a discrepancy between the measured position and the actual position of the limb, and thus the robot should at least as stiff as KINARM to minimize this discrepancy. Finally, Planar MEDARM should be able to accommodate users of a wide range of size. To fit most adult users, the length of the mechanism should have a range of approximately 0.26– 0.37 m and 0.20–0.29 m for the upper arm and forearm limb segments, respectively 关22,23兴. Likewise, the handle position must also be adjustable from 0.06–0.11 m in order to accommodate different size hands.

3

(a)

Planar MEDARM Description

Planar MEDARM 共Fig. 1兲 is a 3DOF exoskeleton robot that provides independent measurement and control of motion at the shoulder, elbow, and wrist in the horizontal plane. The entire mechanism is located underneath the user’s arm, and all joints are actuated by a cable-drive system. All three joint axes are parallel, and the distances between the axes are adjustable to accommodate users with different arm lengths 3.1 Mechanical Design. The joint layout of Planar MEDARM provides a simple solution for multiple mechanical design issues. Figure 2 takes a step-by-step approach to describe the logic behind the final design, and begins by considering the three joint system that the exoskeleton aims to mimic. A cabledriven 3DOF mechanism consisting of a standard serial connection of links with adjustable length, as shown in Fig. 2共a兲, would run into three design issues. Cable tension. A concern with the design of Fig. 2共a兲 is that the cables do not permit free link length adjustments when the actuators are not applying tension. The cables are routed along the links from joint to joint, so changing the length of the links will change the distance between the joints and hence length of cable required to pass along the link. A single link length change can be up to ⬃10 cm, so the cable will be as much as ⬃20 cm too short or too long. This is more than sufficient for all of the cables to fall 021002-2 / Vol. 3, JUNE 2009

(b)

(c)

Fig. 1 CAD drawings of Planar MEDARM: „a… setup with a user, „b… top view, and „c… side view. Actuation cables are not shown for clarity.

off the pulleys entirely if one or both links are shortened. A solution is to guide the cables along passive linkages between each joint, as shown in Fig. 2共b兲. Now, if the limb segment lengths are adjusted to accommodate different size users, the total distance between joint axes does not change. Gravity support and body interference. There are two additional drawbacks for both Figs. 2共a兲 and 2共b兲. The first is that the weight of both the exoskeleton and the limb must be supported at the shoulder joint axis. Providing support only at this point means that a significant bending moment would be applied to the shoulder joint axis at all times. Not only does this put significant force on the shoulder joint bearings, but also, it invariably leads to out-ofplane compliance. The second problem is that all equipment must be attached to or passed across the shoulder joint axis. The torso prevents equipment from being placed directly under the shoulder joint, so all equipment must be placed above the shoulder, resulting in a substantial amount of equipment directly beside the user’s head. Not only can this be claustrophobic for the user, but it also limits the amount and kind of equipment that can be used. For example, for bilateral systems, the presence of this equipment will prevent use with small children because each exoskeleton will interfere with each other. A solution to both of these problems is to introduce a virtual four-bar linkage into the design. First, a circular track on which a low friction carriage can freely move is placed underneath the upper arm so that it is centered on the shoulder joint 共Fig. 2共c兲兲. The carriage contains four wheels that roll along the v-shaped edge of the curved track. Second, all equipment on the shoulder joint axis are moved back and away from the shoulder joint axis. In this case, the passive linkage of the upper arm becomes an Transactions of the ASME

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(a)

shoulder joint

(a) shoulder driving joint

wrist joint

elbow joint

(b) (b)

shoulder joint elbow joint

no wrist joint

(c)

(d)

centre of mass

Fig. 2 Design „a… offers no way to maintain cable length when adjusting the link lengths, provides support only at the shoulder joint axis, and interferes with the user’s body. „b… The passive triangular linkages permit adjustment of the limb segment lengths „in gray with arrows… without the cables falling off. „c… The curved track and carriage underneath the arm ensure that the exoskeleton and the user’s limb are well-supported. The virtual four-bar linkage „dashed lines… that allows all equipment to be moved away from the user. „d… A CAD drawing of the final mechanism is shown without cables for clarity. The center of mass of the exoskeleton is indicated.

active linkage that drives the carriage along the curved track. The combined weight of the exoskeleton and limb is now supported by the carriage 共see center of mass in Fig. 2共d兲兲, and all equipment are moved away from the user. The resulting motion is identical to a four-bar linkage, but there are no physical structures near the shoulder joint axis as indicated by the dashed lines in Fig. 2共c兲. In other words, it is a virtual four-bar linkage. A computer-aided design 共CAD兲 view of the final mechanism is shown in Fig. 2共d兲. In existing cable-driven curved track designs that are used to create a virtual joint axis 共for example, as used by CADEN 7 关24兴 or ARMin II 关10兴兲, the driving joint axis is attached to the carriage. This means that the actuator must move along with the carriage, adding significant inertia and bulk to the mechanism. For Planar MEDARM’s curved track system, the driving joint axis is Journal of Medical Devices

Fig. 3 Top view schematics of „a… Planar MEDARM and „b… KINARM. Planar MEDARM provides planar 3DOF motion „shoulder, elbow, and wrist…, and is driven by a joint that is offset from the shoulder joint axis and that is part of a virtual four-bar linkage. KINARM provides planar 2DOF motion „shoulder and elbow… and is driven directly through the shoulder joint axis, where the elbow is driven by a four-bar linkage „parallelogram…. The shoulder joint axis is the only support point for KINARM, while Planar MEDARM is supported by its curved track.

fixed relative to the track and therefore does not move with the carriage. The actuator is connected to the carriage by a lightweight linkage, greatly reducing the inertia of the system. Planar MEDARM’s structure is similar to KINARM in that both can be described as a four-bar linkage 共see Fig. 3兲. The difference is that Planar MEDARM does not require any physical structures on the shoulder joint axis, whereas KINARM is supported entirely at the shoulder joint axis. An advantage of this new design is that all equipment are moved away from the user, and because there is no longer any interference with the user’s body, the equipment can be placed underneath the arm entirely. An additional benefit of the new design is reduced vertical compliance because the weight of the arm is directly supported by the carriage near the elbow joint axis. Planar MEDARM’s design also allows an actuated DOF at the wrist, which would be a challenge to incorporate into the current KINARM design. In the KINARM design, the actuators are mounted above the user’s shoulder, beside their head, and are both coupled to the shoulder joint axis. Torques are transmitted to the joints of the limb by vertical linkages that are routed from above the shoulder to underneath the limb. The advantage of this design is that the linkages are lightweight. Adding a wrist joint would require additional linkages and transmission components, which would diminish the lightweight advantage that the current KINARM design offers. Furthermore, the shoulder joint is already quite complex because both motors act through this axis, and it serves as the main support for the exoskeleton. Adding another actuator would complicate the system further and would place even more equipment beside the user’s head. In contrast, for Planar MEDARM, adding the third DOF is simply a matter of adding another pulley to each of the existing joint axes. The motors are located behind the user, and thus additional motors have no effect on the user. The shoulder joint 共␪s兲 is indirectly actuated by the shoulder driving joint 共␪sd兲, so it is necessary to quantify their relationship. This can be done by analyzing the mechanics of the closed-loop JUNE 2009, Vol. 3 / 021002-3

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(a)

shoulder joint

UT

shoulder driving joint

FT

H

elbow joint opposite view in (b)

(b)

FL

UL

guide pulley joint Fig. 4 A labeled schematic of the virtual four-bar linkage. ␪o = −20 deg, lo = 0.125 m, lsd = 0.20 m, and lg = 0.25 m. lu is the length of the user’s upper arm, and is a fixed value between 0.26m and 0.37m. ␪sd is the shoulder driving joint angle, ␪s is the shoulder joint angle, and ␪g1 is the guide pulley angle. ␶sd is the torque applied at the shoulder driving joint, and ␶s is the torque that appears at the shoulder joint. Positive angle is defined as counterclockwise from the x-axis.

chain 共see Fig. 4兲. Knowing the link lengths 共lu, lo, lg, and lsd兲, the offset angle 共␪o兲, and any one other angle in the four-bar linkage, the remaining angles can be related. As the shoulder driving joint is actuated 共i.e., known兲, the shoulder angle 共␪s兲 and guide linkage angle 共␪g1兲 can be determined. The relationships are given by Eqs. 共1兲–共4兲

冉

␪s = arctan where

y − lg sin共␪g1兲 x − lg cos共␪g1兲

冉冊

␪g1 = arctan

冊

冉

l2g − l2u + x2 + y 2 y − arccos x 2lg冑x2 + y 2

共1兲

冊

共2兲

x = lo cos共␪o兲 + lsd cos共␪sd兲

共3兲

y = lo sin共␪o兲 + lsd sin共␪sd兲

共4兲

Similarly, a torque at the shoulder is created by applying a torque at the shoulder driving joint using an appropriate scaling factor

␶sd =

冉

冊

lsd sin共␪g1 − ␪sd兲 ␶s lu sin共␪g1 − ␪s兲

共5兲

Equation 共5兲 assumes that no torques are applied at the elbow or guide pulley joints, and thus describes the simplest case in which only shoulder torque is applied. 3.2 User Attachment and Alignment. The user alignment and attachment design is similar to KINARM, and is illustrated in Fig. 5. It is first necessary to align the user’s shoulder joint center 共glenohumeral joint兲 with the robot. For the current prototype, this is achieved through adjustment of the chair position. The upper arm and forearm lengths can be independently adjusted to accommodate users of different size. Upper-arm length can be adjusted by sliding the elbow joint relative to the carriage. A single quickrelease clamp is used to lock the joint in place as shown in Fig. 021002-4 / Vol. 3, JUNE 2009

Fig. 5 „a… A side view of the exoskeleton showing the segment length adjustments for the exoskeleton. The labels are as follows: UL—upper-arm length, FL—forearm length, UT—upperarm trough, FT—forearm trough, and H = handle. „b… A close-up view of the carriage „opposite side view dashed rectangle in „a……, showing the quick-release clamp for the upper-arm length adjustment.

5共b兲. Forearm length can be adjusted by positioning the wrist joint using a telescopic linkage, which is then clamped using thumbscrews 共see Fig. 5共a兲兲. The user is aligned with the mechanism at the upper arm and forearm using molded fiberglass arm troughs, which can be adjusted along the linkages as needed 共see Fig. 5共a兲兲. The system is designed to allow the arm troughs to be easily swapped for different sizes to accommodate a wide range of users. Currently, the subject grasps a handle. The location of the arm troughs and the handle can be fixed with a single thumbscrew clamp, as shown in Fig. 5共a兲. All links are custom machined aluminum to keep the mass and inertial properties low in order to minimize the exoskeleton’s influence on natural limb motion. Each joint has built-in mechanical joint limits to ensure that the robot does not extend the user’s arm beyond physiological limits. 3.3 Actuation System. The core of Planar MEDARM’s actuation system is an open-ended cable-drive transmission and is illustrated in Fig. 6. A cable-drive system was chosen because the motors can be located remotely from the joints. This choice has several benefits. First, cable-drive systems add minimal weight to the structure of the robot, substantially increasing the power-toweight ratio of the actuation system, and reducing the apparent inertia of the robot as seen by the user. Second, with no motors on the linkages, there is less chance of mechanical interference with the user. Finally, the transmission offers significant design flexibility in how the cables can be routed along the mechanism. The choice of cable routing scheme has a significant effect on the performance of the device. There are five unique cable routing schemes for a 3DOF system 关25兴. The schemes were analyzed to find the choice that has the best compromise between having both minimal antagonism between cables 共and hence the most even distribution of forces across the cables兲 and minimal peak forces. Transactions of the ASME

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(a)

(b)

Shoulder Driving Joint

Guide Pulley #1

Elbow Joint

Guide Pulley #2

Wrist Joint

Fig. 6 „a… A CAD drawing and „b… a simplified planar schematic representation of the original cable routing structure. Each of the four cables is denoted by a different line type. Symbols s, ␰, r, ␶, and ␪ represent cable displacement, cable force, pulley radius, joint torque, and joint angle, respectively.

Figure 6 illustrates the routing scheme chosen for this robot. Open-ended cable-drive systems are not new, and the relationship between joint motion and cable motion is well understood 关25,26兴. However, Planar MEDARM’s novel virtual four-bar mechanism requires special modifications to account for the fact that the cables are routed along one edge of the four-bar mechanism. In actual fact, the four cables are routed across four joints 共rather than three兲 because the guide pulley on the four-bar linkage that drives the shoulder also contributes to the motion. The result is that the cables that reach the elbow and wrist joints change length when the shoulder moves. Fortunately, the guide pulley angle is not independent because it is a function of the other angles of the four-bar linkage. The cables also pass around a second guide pulley on the forearm triangular linkage, but this linkage is fixed and thus does not affect the system. Therefore, after some modifications to account for the four-bar linkage, the cable displacement, s, and the change in joint angle, ⌬␪, can be related using Eq. 共6兲

冤冥冤 s1

− rsd

s2

rsd

s3

s4

=

re

− rsd − re rsd

− rw − 1

− re − rw re

where ⌬␪4bar is the added term

1

rw

1

rw

−1

冥冤 冥 ⌬␪sd ⌬␪e

⌬␪w

共6兲

⌬␪4bar

⌬␪4bar = rg1⌬␪sd − re⌬␪s + 共re − rg兲⌬␪g1

共7兲

These relationships are illustrated in Fig. 6共b兲. Note that ␪s refers to the actual shoulder joint, and that ␪sd refers to the shoulder driving joint, which is offset from the shoulder joint axis. Both ␪s and ␪g1 can be calculated from ␪sd using Eqs. 共1兲 and 共2兲, respectively. Changes in cable length are achieved by winding up or unwinding cable from driving pulleys. A cable is clamped to each driving pulley, which is driven by a slotless brushless dc motor 共Compumotor SM Series, Parker Hannifin Corporation, Rohnert Park, CA兲 using a timing belt. Thus, a rotation of the motor either winds up or unwinds the cable from the driving pulley. Each motor has a built-in optical encoder, which is used to calculate the cable length changes. The motor encoders are capable of measuring joint angle in increments of 0.006 deg 共⫾0.02 deg accuracy兲. All Journal of Medical Devices

motors are located behind the user, as shown in Fig. 1. In addition, secondary optical encoders 共Mercury I and II Series, Micro-E Systems, Natick, MA兲 are mounted to each of the three joints to obtain direct measures of the joint kinematics. The elbow and wrist joint encoders each employ a high-resolution rotary glass scale, and the angles can be measured in increments of 0.0001 deg and 0.0002 deg, respectively with an accuracy of ⫾0.005 deg. The shoulder joint encoder measures shoulder angle directly using a tape scale mounted to the outer diameter of the curved track. The large diameter permits measurement of shoulder angle in increments of 0.00004 deg 共⫾0.00002 deg accuracy兲. Using such highresolution secondary encoders permits a much more smooth calculation of joint velocity and acceleration. To apply a set of torques to the joints, calculations must be made to determine what force to apply in each of the cables. The relationship between joint torque and cable force in an openended cable-drive system has been described previously 关25,26兴, but once again, special considerations must be made to account for the contributions from Planar MEDARM’s virtual four-bar linkage. The reason for the modification is that when a torque is applied to the elbow joint, a torque of the same magnitude is also applied at the guide pulley joint. This occurs because the cables are routed around the guide pulley in the same manner as the elbow joint, and therefore a torque is simultaneously applied to the four-bar mechanism. The result is an unwanted torque about the shoulder joint. To correct this problem, an additional torque, ␶4bar, must be applied to the shoulder driving joint whenever an elbow torque is applied, in addition to the properly scaled shoulder torque, ␶s. This relation is defined by Eq. 共8兲

␶sd =

冉

冊

lsd sin共␪g1 − ␪s兲 ␶s + ␶4bar lu sin共␪g1 − ␪sd兲

where ␶4bar is given by:

冉

␶4bar = 1 −

冊

lsd sin共␪g1 − ␪s兲 ␶e lu sin共␪g1 − ␪sd兲

共8兲

共9兲

Note that in Eqs. 共8兲 and 共9兲, the denominator will not go to zero. The link lengths of the four-bar linkage were chosen such that ␪g1 ⫽ ␪sd for the entire range of motion for all upper-arm lengths. In fact, the linkages in this mechanism conform to the requirements for a Grashof linkage 关27兴, which mean that the links connected to the smallest link 共in this case, the fixed link兲 can both rotate 360 deg without reaching singularity. Therefore, applying a torque at the shoulder driving joint will always produce a torque at the shoulder joint. The cable force, ␰, and joint torque, ␶, can then be related using Eq. 共10兲:

冤冥冤

− rsd rsd − rsd rsd ␶sd ␶e = re − re − re re − rw − rw rw rw ␶w

冥冤 冥 ␰1 ␰2 ␰3 ␰4

共10兲

where ␶sd is the total torque to be commanded to the shoulder driving joint, as defined by Eq. 共8兲. The scaling factor in Eq. 共8兲 is determined from Eq. 共5兲. It should be noted that with an elbow torque command of zero, ␶4bar becomes zero, and therefore ␶sd reduces to a single term that describes the applied shoulder torque. Thus, Eq. 共10兲 must be used with Eqs. 共8兲 and 共9兲 to determine what force to apply in each of the cables to apply torques at Planar MEDARM’s joints. However, because the system is overactuated, there are an infinite number of solutions for a given set of joint torques. A practical solution that ensures that the cables are always under tension and that positive force is always applied can be obtained using the torque resolver technique 关25兴. This solution includes a constant pretension force in the cables that prevents the cables from becoming slack, even when the mechanism is moved passively without any joint torques applied. As such, the motors must always be supplying at least this constant torque. To prevent JUNE 2009, Vol. 3 / 021002-5

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the cables from becoming slack when the system is turned off or during a power failure, each motor is equipped with an electric brake. 3.4 Electronics and Control. The present motion control system used for this prototype is basic. Each motor is powered by a servo drive amplifier 共Compumotor Gemini GV Series, Parker Hannifin Corporation, Rohnert Park, CA兲 operating in torque mode such that the motors provide a constant torque proportional to a ⫾10 V command. The drives are wired with a single switch that disables all drives in the event of an emergency. Additionally, the drives route the power to the motor brakes so that the brakes engage when the drives are disabled or a fault is detected. As mentioned in Sec. 3.2, each joint contains mechanical joint limits to prevent the robot from pushing the limb beyond safe physiological limits. The heart of the system is a motion control card 共PMAC, Delta Tau Data Systems Inc., Chatsworth, CA兲 mounted in a computer. The motion control card receives the quadrature encoder signals from the four motor encoders and three secondary encoders as input. The output is simply four ⫾10 V analog torque command signals, which are sent to the four servo drives. Presently, the motion control card is programmed directly with all instructions necessary to calculate joint kinematics and to apply joint torques. While basic control algorithms have been hard-coded into the motion control card, a custom software package is required to apply more advanced control and data handling. The DEXTERIT-E software package 共BKIN Technologies, Kingston, ON, Canada兲 was adapted to allow simple data collection from Planar MEDARM. 3.5 Dynamic Model and Simulation. A dynamic model was created for Planar MEDARM in MATLAB based on the robot toolbox 关28兴. The model was defined as a standard rigid-body manipulator with negligible cable dynamics. Dynamic parameters of the exoskeleton were estimates from CAD drawings, and upper-limb parameters were calculated from anthropometric data tables based on user height and weight 关22,23兴. The model first calculated the joint torques required to achieve a given trajectory. The cable forces required to generate these joint torques were then calculated using the torque resolver technique 关25兴. All forces and nonaxial moments at each joint were also calculated. Simulations were performed for various reaching movements with a peak end-point velocity of 1.0 m/s 关29兴. Movements included single-joint motion through each joint’s full range, and a variety of multijoint reaching movements. The simulations were used to determine the range of forces/torques that would occur during these movements, which were in turn used to select appropriate motors, gear ratios, cables and joint bearings. Peak joint torques of ⫾5 Nm, ⫾2 Nm, and ⫾0.5 Nm for the shoulder, elbow, and wrist, respectively, were found to be sufficient for movements of this type. These torques are much smaller than would be required for movements out of the horizontal plane because Planar MEDARM does not need to overcome gravity, and thus the risk of injury is significantly reduced.

4

Performance Evaluation

A prototype of Planar MEDARM has been fully assembled 共Fig. 7兲. Before any tests were performed, the secondary encoders at the joints were used to confirm that the joint angle calculations from the motor encoders were correct. Also, the motors and servo amplifiers were calibrated to ensure that the torque output would be as expected and consistent across all four motors. Calibration of motor output is particularly important in this type of robot as the four cables require constant pretension to be applied by the motors. Small differences between the motors lead to the application of a small torque at one or more of the joints. Several fundamental performance parameters of the prototype have been measured including: joint friction, inertia as seen at the joints, joint compliance, and vertical 共out-of-plane兲 compliance. These parameters are related to one another, thus compromises 021002-6 / Vol. 3, JUNE 2009

Fig. 7 A photo of the fully constructed Planar MEDARM prototype in its original configuration. The view was chosen to match the CAD view from Fig. 1.

must be made. Planar MEDARM is primarily an assessment tool for upper-limb motion, and as such, it must influence natural motion as little as possible. Therefore, for this application, achieving both low friction and inertia is more important than achieving low compliance. In fact, little can be done to reduce the total compliance in the system because the interface between the limb and the robot is inherently compliant due to the layers of soft tissue, and can dominate the overall compliance. In terms of the exoskeleton itself, as long as bending of the linkages is not the dominant source of compliance, the secondary encoders at the joints will reduce much of the problem associated with compliance because the position of the robot will be more precisely known. Data collection has also been tested by collecting several samples of experimental data using Planar MEDARM. A goal of Planar MEDARM is to extend the capabilities of KINARM, so the performance measures are compared directly to those of the KINARM where possible. The following is a brief description of the testing parameters and the methods used to obtain measurements. 4.1 Measured Parameters. Joint friction. Friction in a robotic system can have both beneficial and detrimental effects on performance. Friction can provide a level of damping that helps to stabilize the system under position control. However, a high amount of friction affects natural passive motion of the user, which can interfere with unaided natural reaching movements. The main application of this robot is measuring motor performance of a user. This application demands smooth and effortless operation of the device and therefore, low friction is desirable. To obtain an idea of the levels of friction that a user would see at each joint of the exoskeleton, static friction was measured. Static friction can be measured by determining the minimum torque required to create a movement at the joint. Friction is a highly variable parameter that is influenced by many aspects of the system, therefore the friction was measured for several configurations across the range of motion of the joint, and an average friction torque measurement was obtained. The accuracy was determined by finding the maximum and minimum friction values for the entire joint range of motion. It was determined that the static friction measurements are accurate to within ⫾0.05 Nm. Torque ripple created by the servo drives was the dominant source of error. Inertia. The inertia of the exoskeleton, as seen by the joints of the user, also has a significant impact on the performance of the system. In this paper, the phrase “inertia as seen by a joint of the user” refers to the inertia of all components of the exoskeleton and motor system a user feels when they move that joint with other joints fixed. For example, the “inertia as seen by the elbow” includes the inertia of all distal components of the exoskeleton 共i.e., the forearm, wrist, and hand components兲, and the inertia of the pulleys, gears, and motors that move during elbow motion. Ideally, from an experimental point of view, the inertia should be Transactions of the ASME

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zero, but of course this is not possible. More practically, the mass and inertia of the exoskeleton should be kept as low as possible, and the joint inertias should be proportional to the joint inertias of the human upper-limb. Otherwise, the device will have a significant effect on the natural intersegmental dynamics of the limb. Minimum and maximum inertias were estimated from the detailed CAD drawings used to manufacture the prototype for the minimum and maximum segment lengths, as indicated in Sec. 2. The gear ratio and the number of motors driving the joint were incorporated into the calculations. All calculations specified a shoulder angle of 45 deg, an elbow angle of 90 deg, and a wrist angle of 0 deg, corresponding to a typical starting point for a reaching task. Considering that manufacturing processes typically produce parts with a tolerance of ⫾0.1 mm 共at most兲, it is expected that the actual inertia values are within approximately 1% of the CAD estimates. Another source of error arises from neglecting cable mass in the estimates. Compliance. Compliance has an impact on the overall performance of a robot. With high compliance, tight position control is challenging, and it is not possible to accurately measure true joint angles. This is a result of the elasticity of various components of the system. Sources of compliance include elasticity of cables and belts, and bending of shafts and linkages. In-plane joint compliance was measured by reading the change in position noted by the motor encoders while commanding a joint torque to the system with all joints locked in place 共using c-clamps and/or screws兲. The effective torsional spring constant 共i.e., stiffness and hence compliance兲 could then be easily calculated from Hooke’s Law. The joint torque was applied in 0.5 N m increments up to the maximum output of the motors. Note that for Planar MEDARM, the joint compliance can be different for positive and negative rotations due to the distribution of the cables, but in this paper, the average is presented. The compliance values presented here are based on measurements of cable length change 共motor encoder readings兲, torque, and pulley radii, each of which has an associated measurement error. Propagating these errors through the calculations leads to a compliance accuracy of ⫾9%. The largest source of error comes from the cable displacement measurements, which are limited by the accuracy of the motor encoders. Vertical compliance was measured by placing known masses at the wrist joint and observing the resulting vertical displacement. The system was configured with a shoulder angle of 45 deg, an elbow angle of 90 deg, and a wrist angle of 0 deg, with an upperarm length of 0.30 m and a forearm/hand length of 0.25 m 共Planar MEDARM’s wrist joint was locked because KINARM does not have a wrist joint兲. Once again, this configuration corresponds to a typical starting point for a reaching task, so it is a reasonable point of comparison. Accuracy of the vertical compliance measurements is ⫾1%. The main source of error is the vertical distance measurement. Reaching task. To assess its ability to monitor limb motion, Planar MEDARM was set up to perform one of the basic tasks that is performed in motor control research—the center-out reaching task 关30,31兴. A simple 2D virtual display was built to project visual targets in the plane of the robot 共see Fig. 8兲. The display is capable of presenting to the user any one of eight peripheral targets equally spaced around a 10 cm radius circle, as shown in Fig. 8共c兲. Several normal, healthy volunteers were recruited to perform this experiment to test out the robot’s measuring abilities. The system was calibrated so that the starting point for the user 共central target兲 was located such that the handle of the exoskeleton corresponded to the limb configuration in which the shoulder and handle were aligned at x = 0 and that the elbow was 90 deg and the wrist was 0 deg 共Fig. 8共c兲兲. The subject was directed to move as quickly and as accurately as possible from the central target to the peripheral targets as they appeared one at a time in the display. After reaching the target, the subject moved back to the central target. Planar MEDARM recorded the three joint angles during Journal of Medical Devices

(a)

LED Panel

SemiTransparent Mirror

(b) LED Mirror Image of LED

(c)

1 8

2

7

3 4

6 5

Fig. 8 „a… Planar MEDARM’s virtual display includes a basic structure that holds a semitransparent mirror and a set of LED lights above the workspace. „b… The mirror is placed equidistant from the working plane of the robot and the LEDs so that the user can see their limb and an image of the LED in the same plane. This system allows unrestricted access to the workspace. „c… The visual display system was used to present the subject with a reaching task which involved making movements from the center target „black circle… to one of the eight outlying targets „hollow circle, 10 cm distance….

the outward movement. Each target was displayed a total of ten times, in random order. DEXTERIT-E 共BKIN Technologies, Kingston, ON, Canada兲 was used to develop the experimental protocol and to collect the data. Viscous load stability. To demonstrate the ability of Planar MEDARM to apply joint torques, a viscous loading test was performed. A viscous load is a simple load that opposes motion at a joint with a magnitude proportional to the velocity of the joint, as given by JUNE 2009, Vol. 3 / 021002-7

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␶i = − Kv␪˙ i

共11兲

where ␶i is the torque applied to joint i, Kv is the velocity feedback gain, and ␪˙ i is the joint angular velocity of joint i. Robots tend to become unstable when velocity feedback loads exceed a certain magnitude. The stability is influenced by several aspects of the mechanical design, such as the resolution of the encoders 共i.e., quality of the velocity signal兲, and flexibility 共inplane compliance兲 in the robot. Increasing the velocity feedback gain amplifies this problem, and ultimately can cause unstable oscillatory motion. In general, friction will help to dampen any oscillations, but because this type of robot is designed to have low friction, these robots are often limited in the magnitude of viscous loads that can be applied. This has far-reaching consequences that limit not only the maximum magnitude of viscous loads, but also the ability to apply other force fields or position control. To test the stability of Planar MEDARM under viscous loading conditions, velocity feedback torque was applied to each joint individually using Eq. 共11兲, while moving the robot around the entire workspace using both smooth and abrupt movements. The highest velocity feedback gain, Kv, that could be applied without any amount of instability was recorded. Instability involved oscillatory motion of the motors, and would typically first manifest as tiny vibrations, which could be felt at the robot’s handle. The test was performed using the velocity signal, as calculated from the motor encoders, and again using the secondary encoders. In both cases, the velocity signal was filtered using a second-order Butterworth filter with a 10 Hz cut-off frequency for comparison with existing KINARM data. 4.2 Testing Configurations. In order to get a better idea how the above performance measures are affected by the components and specific design features of Planar MEDARM’s actuation and transmission system, the parameters were measured for several variations in the actuation system. Starting with the original design 共as described in Sec. 3兲, changes were made one at a time, but each consecutive variant maintained the changes from the previous systems. So in the end, the final system consisted of all changes. Each modification was chosen to upgrade the performance of the system without requiring any structural changes or changes to the prototype’s overall mechanical design. System a: original. The original design was tested first. The main parameters included a gear ratio of 6 共3 from belts and 2 from cable pulleys兲, a cable routing structure, as in Fig. 6共b兲, a pulley diameter of 60 mm, and a cable diameter of 1.19 mm. System b: gear ratio. The goal of this first change was to reduce both the friction and inertia of the motor system. The overall gear ratio was reduced to 2 共3 from belts and 2/3 from cable pulleys兲 by adding an adapter to the cable-windup system. The adapter provided a 90 mm diameter pulley to wind up the cable, whereas the original system used a 30 mm diameter pulley. System c: cable routing. The goal of the second change was to further reduce the overall friction and inertia about the wrist and elbow joints. An alternate cable routing structure was implemented to drive the joints 共Fig. 9共a兲兲. While the original structure had the lowest and most even force distribution, it required all four cables to span all three joints. In contrast, the new structure needed only two cables for the wrist, three for the elbow and four for the shoulder. System d: thicker cable. The primary goal of this third change was to decrease the compliance by increasing the thickness of the cables. Doubling the cable diameter from 1.19 mm to 2.38 mm, increased the cross-sectional area of the cable by a factor of 4, and therefore reduced compliance of the cable by a factor of 4. System e: 2DOF. The fourth change was to convert the system to a 2DOF robot to allow a more direct comparison with KINARM. The wrist joint was still present 共but locked兲, but it was not actuated because the cables were removed from the wrist joint entirely. Note that the secondary encoder at the wrist could still measure wrist position, even though the joint was not actuated. 021002-8 / Vol. 3, JUNE 2009

(a)

Shoulder Driving Joint

Guide Pulley #1

Elbow Joint

Guide Pulley #2

Wrist Joint

Shoulder Driving Joint

Guide Pulley #1

Elbow Joint

Guide Pulley #2

Wrist Joint

(b)

Fig. 9 Planar schematic representation of „a… the alternate cable routing structure of system c and „b… the 2DOF structure of system e. In „a…, there are four cables at the shoulder, three at the elbow, and two at the wrist. In „b…, there are three cables at the shoulder, two at the elbow, and zero at the wrist „free to rotate….

Only three cables were required to drive the shoulder and elbow joints, and therefore the cable structure was updated using the only possible structure for a 2DOF system with three cables, as shown in Fig. 9共b兲. System f: KINARM. As a base of comparison, the same parameters were measured for KINARM. No special changes were made to KINARM, so all testing parameters were measured for both the shoulder and elbow. Although the motors themselves were not changed, the changes made to the actuation system had a direct effect on the magnitude of torque that can be applied to each joint. Table 1 summarizes the peak torque that can be produced at each joint for each testing configuration. 4.3 Results. Measurements of joint friction are shown in Fig. 10共a兲 for all systems. Friction was initially several times larger than KINARM, but it is clear that the changes provided a substantial reduction in friction. The biggest improvement occurred for system b when the gear ratio was changed. The friction was nearly halved for all three joints. This makes intuitive sense because reducing the gear ratio by a factor of 3, reduces the friction of the motor system 共the motors themselves and the timing belts兲, as seen by the joints by a factor of 3. Since all four motors are connected to all three joints, this is a substantial reduction. Another substantial reduction in friction occurred for the elbow and wrist when switching the cable routing structure 共system c兲. This Table 1 A summary of the peak joint torque that can be applied to the joints in the various configurations of Planar MEDARM and KINARM Peak torque 共Nm兲 Configuration

Shoulder

Elbow

Wrist

a-original b-gear ratio c-cable routing

⫾37 ⫾11.5 ⫾5.75

d-thicker cable

⫾5.75

e-2DOF

+5.75 ⫺12.5 ⫾12

⫾37 ⫾11.5 +5.75 ⫺12.5 +5.75 ⫺12.5 +6.15 ⫺5.75 ⫾12

⫾37 ⫾11.5 +5.75 ⫺2.85 +5.75 ⫺2.85 N/A

f-KINARM

N/A

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Joint Friction (Nm)

(a) 0.75

0.50

0.25

0

a b c d e f Shoulder

a b c d e f Elbow

Inertia (kgm2)

(b) 0.75

Joint Compliance (rad/Nm)

0.03

0.50

0.02

0.25

0.01

0

(c)

a b c d Wrist

a b c d e f Shoulder

a b c d e f Elbow

a b c d e f Shoulder

a b c d e f Elbow

0

a b c d e Wrist

0.06

0.04

0.02

0

a - Original b - Gear Ratio

c - Cable Routing d - Thicker Cable

a b c d Wrist e - 2 DOF f - KINARM

Fig. 10 Overall „a… joint friction, „b… inertia as seen by the joints, and „c… compliance at the joints for all variants of the prototype. In „a…, the dark and light gray bars for the shoulder joint indicate the total measured friction with the original and new carriage designs, respectively. In „b…, the dashed lines represent the estimated inertia of limbs corresponding to the minimum and maximum size of Planar MEDARM. The bottom and top of the bars indicate the estimated inertia of the exoskeleton when set up for the smallest and largest arms, respectively. In „c…, the total height of the bars indicates the total measured compliance of the exoskeleton. The light portion of the bars indicates the estimated contribution of the cables to the measured compliance.

reduction cut the friction at the wrist in half simply by removing two cables 共including pulleys, belts and motors兲 entirely from the wrist drive system. Similarly, the elbow was reduced by a quarter because one of the four cables was removed. For system e, the wrist joint friction was not measurable using our approach as the only possible source of friction is a pair of bearings on the wrist joint shaft. It should be noted that moving from system a to system c, the friction was reduced by similar magnitudes at each joint. However, the reduction in friction of the wrist joint is most perceptible by the user. For systems c–e, the friction at the elbow was reduced to a magnitude comparable with KINARM. Similarly, the wrist exhibJournal of Medical Devices

ited low friction. In contrast, the shoulder joint has substantially higher friction. An estimate of the friction in the curved track system indicates that about half of the measured friction 共in systems b–e兲 comes from the curved track and carriage. The track system was designed for heavy-duty industrial use, and the carriage wheel surfaces are flat to help distribute the forces on the track. This design forces the wheels to slide against the track surface as they rotate, which increases friction and audible noise. As a subsequent test, a custom carriage that achieved point contact with the track was designed to resolve this issue. The new carriage has reduced strength when compared with the original design, but it remains sufficient for this application. Friction of the new carriage on the track was reduced by 0.1 N m to 40% of its original value, and the audible noise level was also reduced. This reduction in friction is indicated by the light gray bars in Fig. 10共a兲. The remaining friction at the shoulder is primarily a result of the motor system. Figure 10共b兲 shows the estimates of the inertia, as seen by the joints. The length of the bars for each system shows the estimated range of inertia for the robot. The bottom of the bar indicates the inertia for the exoskeleton when set up for the smallest arm 共corresponding approximately to a person 1.4 m in height兲, and the top of the bar is for the largest arm 共2.0 m in height兲. The exoskeleton can be adjusted anywhere in between this range. The dashed lines in the plots indicate the estimated inertia of limbs corresponding to the minimum and maximum size of Planar MEDARM. It is clear that except for the wrist joint in system a, the inertia of the robot is similar to the inertia of the human limb. After reducing the gear ratio of the system and changing the cable routing structure, the apparent wrist inertia dropped dramatically. In systems c and d, both the elbow and wrist joint inertias lie within the lowest range of the human limb. So, in the worst case, for the smallest person, the inertia of the robot is roughly equal to the inertia of their limb at the elbow and wrist. However, the shoulder joint inertia is disproportionately higher than the elbow and wrist when viewed relative to the human limb, and the changes had little effect. This is a result of the heavy carriage used in the curved track mechanism. The shoulder inertia of Planar MEDARM is higher than KINARM, while its elbow inertia is marginally less. In-plane joint compliance is shown in Fig. 10共c兲. The total height of the bars is the measured compliance, while the light gray portion indicates the estimated contribution of the cables to the measured compliance. It is clear that changing the gear ratio and cable routing scheme both increased the compliance of Planar MEDARM overall. This occurred because the larger pulley winding up the cables causes more cable length change for a given rotation, and there are fewer cables attached to the elbow and wrist joints. In system d, upgrading to the thicker 共and stiffer兲 cable helped to reduce the compliance, but this reduced only the compliance contributed by the cables themselves. The large proportion of dark gray in the bars for system d indicates that the large majority of the compliance 共⬃90%兲 comes from something other than the cables. One source of compliance is the timing belts, but the major source is the structure of the mechanism itself. There are several points in the system that visibly bend when loads are applied. These structural elements include the main support beam, the wrist joint axis, and the elbow joint axis. The cable compliance in system d is less than KINARM’s total compliance, so there is potential to reduce the compliance to comparable levels. One of the advantages of Planar MEDARM’s design over KINARM is the solid support against gravity that the curved track provides. Indeed, the vertical compliance measured for Planar MEDARM is 0.047 mm/N, while for KINARM it is 0.132 mm/N, as shown in Fig. 11. Planar MEDARM is three times stiffer than KINARM for out-of-plane motion. It was visually apparent that most of the measured compliance is a result of the elbow joint JUNE 2009, Vol. 3 / 021002-9

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(a) 0.1

0.10

0.05

0

(m)

Vertical Compliance (mm/N)

0.15

0

Planar MEDARM

KINARM

Fig. 11 Results of the vertical compliance test, comparing Planar MEDARM with KINARM

-0.1

5

Conclusions and Future Work

Planar MEDARM is an upper-limb robotic exoskeleton that is designed as a possible revision for KINARM. The prototype is based on a novel mechanical design that makes use of a cabledriven curved track mechanism which allows all equipment to be 021002-10 / Vol. 3, JUNE 2009

-0.1

(b) 70 Angle (˚)

bending. The reaching experiments were run primarily as a qualitative test 共no numerical analysis was performed兲 to see how users perceived Planar MEDARM during use. It is important that the exoskeleton feels comfortable and natural for the user. The test was performed to make sure that users were able to make smooth and straight reaching movements, which are an indication of whether or not the exoskeleton is unduly influencing normal motion. When asked about how it feels to use the robot, subjects noted that it was comfortable, but some subjects pointed out that there is an audible noise while moving the shoulder 共using original carriage design兲. This noise is generated by the carriage on the track, and is a result of the friction in the system. The new carriage design significantly reduced the audible noise. Figure 8共c兲 shows the basic setup for the reaching task. Figure 12共a兲 shows the recorded hand path for all ten trials to each of the eight targets for a single subject. As expected from previous reaching experiments, the results exhibit relatively straight trajectories with a certain amount of trial-to-trial variability depending on movement direction 关31兴. Figure 12共b兲 shows a sample of the recorded joint motion for a single trial reaching to target 1. This confirms that all three joints are indeed contributing to limb motion. The maximum velocity feedback gain for each joint is shown in Fig. 13. The first note to make is that using the secondary encoders 共Fig. 13共b兲兲 allowed equal or higher viscous loading for all cases when compared with using the motor encoders 共Fig. 13共a兲兲. This is expected because the high-resolution secondary encoders allow a much more smooth 共less noisy兲 measure of velocity than the motor encoders. Another expected trend that is readily apparent is that the maximum viscous loading gain decreases for consecutive configuration changes: systems a-c. This coincides with the reduction in friction at the joints seen in Fig. 10共a兲. This reduction in viscous loading capability is particularly noticeable at the wrist joint, because the wrist joint friction was reduced substantially. In addition, the shoulder joint exhibits enough friction and stiffness that the maximum torque limits of the motors were reached before instability was apparent. A final note is that the maximum viscous load increased substantially for system d. The thicker cable increased the stiffness of the system, making it more difficult to excite oscillatory motion. In the final 3DOF configuration 共system d兲, the performance of Planar MEDARM was similar to KINARM even when the motor encoder signal was used. Using the secondary encoders increased the performance of the 2DOF configuration 共system e兲 to a level comparable with KINARM.

Shoulder

0 (m) 90

Elbow

0.1

20

60

80

10

50

70

0

40

60

-10

0

0.5 1 Time (s)

0

0.5 1 Time (s)

0

Wrist

0.5 1 Time (s)

Fig. 12 Results of a basic reaching experiment using the Planar MEDARM. „a… The hand path traces for all trials are plotted. „b… The joint angle profile for one of the trials to target 1.

placed underneath the user’s arm. This mechanical design is invaluable from a clinical perspective because it can accommodate a wider range of people, including small children, while providing greater access to the limb by the clinician. Additionally, Planar MEDARM includes an actuated wrist joint, which enables the device to answer new scientific questions about upper-limb movement. Performance testing indicates that Planar MEDARM performs as well as KINARM in most respects, despite the added functionality and new mechanical design ideas. All tested configurations exceed the specified minimum required torque for each joint. While the final configuration of Planar MEDARM has lower peak torque capability than KINARM, the motors could easily be upgraded to provide more torque. Friction and inertia, as seen at the elbow for Planar MEDARM, are comparable to KINARM, and these same parameters for the wrist are equally acceptable. However, Planar MEDARM’s shoulder joint lags behind. The main area for improvement lies in the carriage, which is the main source of friction, inertia, and audible noise for the shoulder joint, but these shortcomings should not be insurmountable. The custom carriage design was a substantial first step to improving the performance of the carriage. Friction was reduced by 60%, and audible noise was also significantly reduced. The new carriage design did not address the issue of inertia. High inertia at the shoulder is a direct result of the mass of both the carriage and the guide pulleys on the driving linkage. With all of this weight displaced far from the center of rotation, it is not surprising that the inertia is high. Removing one of the carriage’s four wheels 共the most massive components兲, combining the carriage and upper-arm linkages into a single piece, and using smaller guide pulleys would reduce the shoulder inertia by at least 25% bringing the inertia much closer to proportion with the other Transactions of the ASME

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(a)

7

Velocity Gain (Nm•s/rad)

6 5 4 3 2 1 0

Velocity Gain (Nm•s/rad)

(b)

a b c d e f Shoulder

a b c d e f Elbow

a b c d Wrist

a b c d e f Shoulder

a b c d e f Elbow

a b c d Wrist

7 6 5 4 3 2 1 0

a - Original b - Gear Ratio

c - Cable Routing d - Thicker Cable

e - 2 DOF f - KINARM

Fig. 13 Results of the viscous load stability tests, comparing Planar MEDARM with KINARM. The highest velocity feedback gain that can be applied to each joint for each configuration using the velocity signal provided by „a… the motor encoders and „b… the secondary encoders.

joints and with KINARM. This reduction would not affect the other joints. Also, it is important to note that about 40% of the inertia, as seen at the shoulder, is from the addition of the third link and all of the pulleys needed to actuate the wrist joint. Considering that Planar MEDARM was designed specifically to add a wrist joint and to place the support point for the mechanism away from the joint axis, it is a substantial achievement to maintain joint inertia on the same level as KINARM. While the inertia can easily be reduced, reducing friction further may be more challenging. Removing one wheel from the carriage will reduce the bearing friction by 25%, but this would reduce the friction at the shoulder by only about 10–15% overall. Planar MEDARM’s in-plane compliance is higher than KINARM for all joints. Nevertheless, it is important to note that the overall compliance of the system is not dominated by the cables that drive the system. This means that the compliance can be reduced relatively easily by stiffening a few key structural components, and therefore the high compliance is not due to a limitation of the conceptual design. While already significantly less than KINARM, the vertical compliance will be further reduced by these structural upgrades. Once the structural upgrades are implemented, beam bending is reduced, and the remaining compliance will be dominated by the cables and the timing belts used in the motor system. In this situation, the main problems associated with high in-plane compliance are diminished when secondary encoders are added to the joints because the true joint angles are known. In the case of Planar MEDARM, the secondary encoders also remove the need to perform some of the four-bar linkage calculations during operation. Furthermore, the secondary encoders increased the stability of the robot while applying feedback-based loads to the joints. With a stiffer structure, the Journal of Medical Devices

stability could be further improved. Although these encoders are expensive, the ability to include them presents a useful advantage in measuring joint kinematics. Planar MEDARM has successfully achieved its goal to incorporate a wrist joint into the system. It appears from the initial reaching movement tests that Planar MEDARM does not affect limb motion in an adverse way. Furthermore, its performance compares favorably with KINARM, and any problems appear to have feasible solutions. As well as providing a means of extending the capabilities of KINARM, the goal of this prototype was to test the feasibility of using the curved track design to replicate motion at the shoulder girdle. The sternoclavicular joint of the shoulder girdle is much more challenging to actuate than the glenohumeral joint of the shoulder because it is centrally located on the body, and even closer to the head. The curved track system would allow this joint to be actuated from a point offset from the joint itself. The design process is nearing completion for a new 6DOF robotic exoskeleton called MEDARM that will provide independent control of all five major DOFs of the shoulder 共including the shoulder girdle兲, and 1DOF at the elbow 关32,33兴. The Planar MEDARM prototype has already proved an invaluable insight into the future development of KINARM, and the results presented in this paper can also be transferred directly to the MEDARM design.

Acknowledgment The authors would like to thank Luke Harris for machining parts for Planar MEDARM. His experience and contributions to the design process had a significant influence on this work. This work was supported by the Canadian Institutes of Health Research 共CIHR兲, and the Natural Sciences and Engineering Research Council of Canada 共NSERC兲.

Nomenclature ␶i l ␪i ␪˙ i si ⌬␪i ri ␰i Kv

⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽

torque applied to joint i length of linkage i angular position of joint i angular velocity of joint i change in length of cable i change in angular position of joint i radius of pulley at joint i force in cable i velocity feedback gain for viscous load

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