IEEE-International Conference on Mechatronics, ICM 2009 Malaga, Spain
A Design Approach for a New 6-DoF Haptic Device Based on Parallel Kinematics Khan Suleman(
[email protected])
Kjell Andersson(
[email protected])
Jan Wikander(
[email protected])
KTH Royal Institute of Technology, School of Industrial Engineering and Management Department of Machine Design SE-100 44 Stockholm, Sweden.
KTH Royal Institute of Technology, School of Industrial Engineering and Management Department of Machine Design SE-100 44 Stockholm, Sweden.
KTH Royal Institute of Technology, School of Industrial Engineering and Management Department of Machine Design SE-100 44 Stockholm, Sweden.
Abstract— This paper presents an approach to a methodology for design, analysis and optimization of haptic devices. This approach roughly divides the design process into; device requirements, conceptual design, device design, control design and finally building a prototype of the device. In addition, we have applied the first two phases of this methodology, i.e. device requirements and conceptual design on the development of a new 6-DoF haptic device. The intended application area for this device is medical simulations and this research is one important component towards achieving manipulation capabilities and force/torque feedback in six degrees of freedom during medical simulations. Three candidate concepts, all based on parallel kinematic structures, have been investigated and analyzed. The performance parameters being analyzed have covered workspace analysis and force/torque requirements to fulfill the specified TCP force performance. The initial analysis of these three concepts has shown, after a smaller modification of one of the concepts that all concepts seem to satisfy the initially stated requirements. Keywords-component; Design methodology, Haptic devices; Design requirements; Parallel kinematic structure, Modeling and simulation.
I.
INTRODUCTION
A haptic device is a robot-like mechanism that provides a link between a human operator and computer–generated virtual world or a slave mechanism in a remote environment. It reflects forces and torques based on what the operator discovers and interacts with in the virtual or remote world e.g. for use in medical simulations or teleoperation. A bilateral haptic master device can transmit data (typically motion references) from an operator to a slave, and from a slave to an operator (typically force feedback). A haptic feedback system is the engineering answer to the need for interacting with remote and virtual worlds [6]. Haptic feedback is currently a less developed modality of interacting with remote and virtual worlds compared with visual and auditory feedback. The work described here is related to the use of haptics in applications of medical simulation. The research on the haptic device is one important component towards achieving manipulation capabilities and force/torque feedback in six degrees of freedom during simulation of surgical procedures in hard tissue such as bone structures [1]. Such procedures involve removing bone by drilling or milling, including the processing of channels and cavities. Another application field of similar nature is dentistry and dental surgery.
A.
Motivation The application context, surgery in bone structures, leads to two main haptic device requirements that are not simultaneously met by any commercially available device that we have found. These main requirements are: •
Haptic feedback in six degrees of freedom to allow both force and torque feedback from a virtual tool operating in a (narrow) channel or cavity.
•
Device stiffness and force/torque performance that allows realistic simulation of stiff tool-to-bone contacts.
The mechanical structures that currently are used for devices with similar characteristics include serial as well as parallel structures. However, parallel kinematic structures have some significant advantages compared to serial ones, e.g. high stiffness, high accuracy, low inertia with the actuators located on the fix base, thus enabling high transparency. While the device development is interesting and worthwhile in itself, this work is also oriented towards a more general methodology for design, analysis and optimization of haptic devices. B. State of the art Research on the development of haptic devices has been conducted from the late 1940s. Many six degree of freedom haptic devices have been developed; some of these have been commercialized [7]. The Phantom device developed by Massie and Salisbury in 1995 led to major developments to the field of haptics [5]. This device is based on a serial mechanism that can provide enough workspace but not enough stiffness to deal with stiff surfaces of the kind targeted in this work. The HAPTION Virtouse 6D35-45, and MRB Technologies Freedom 6S are serial 6-DoF haptic devices with suitable workspace [12,13] for our application but the problem with these devices are insufficient force/torque capacity and stiffness. Haptic devices using parallel mechanisms have been proposed by many researchers. The Delta and Omega 6-DoF devices by Force Dimension, the modified Delta device and Haptic master proposed by Tsumaki and a new 6-Dof haptic device for desktop application proposed by Lee are based on parallel mechanisms [8, 9,14,15]. These devices have either too limited workspace, too high inertia or too limited stiffness to be used with stiff contacts. On the other hand, a 6-DoF Haptic Cobot [4] has enough stiffness but the size (footprint) and
IEEE-International Conference on Mechatronics, ICM 2009 Malaga, Spain weight are not suitable for the medical applications in question. Some research efforts have been made to use cable driven actuation system instead of mechanical actuators to reduce the inertia of the system [10,11]. But in these concepts the use of strings tension to provide forces, cannot provide appropriate forces at certain locations within the frame. Comparison of specifications of a selection of 6-7 degree of freedom haptic devices; for example peak and continuous forces, torques, approximate rotational and translational workspaces, and the maximum values for structural stiffness or displayable virtual stiffness, are available in [4,7]. II.
DESIGN METHODOLOGY
An initial literature review [7] of haptic input-output devices has been performed to identify candidates for being the best structure for the task at hand. Basically, haptic devices present a difficult mechatronic design problem, as they are required to be backdrivable and light (low inertia), as well as being able to provide enough stiffness, feed back forces and torques when reflecting forces from stiff contacts. Fidelity and structural transparency is required so that the user feels only the dynamics of the virtual or remote interaction being represented and not that of the structure of the haptic device. In this work, a methodology is developed for a more systematic design and optimization procedure for haptic devices. This methodology provides a parametric model based design approach that leads to easier design space exploration and initial verification of the conceptual model The first stage of the methodology is to define the more direct device requirements. These include on a course level: number of DoFs, workspace, stiffness (structure and control), force control dynamics and force/torque capability. The second stage of the methodology is conceptual design (kinematic structure) of the device. Here, the methodology should include preliminary analysis of the workspace, actuator requirements and singularity points (which cannot be within the workspace). After conceptual design follows device design which includes design of the mechanical structure, design of actuation and transmission, and analysis of workspace, stiffness, force torque capabilities and backdrivability. Once the mechanics and actuation are designed the models necessary for control design can be derived. This is done upon entering the control design stage in which sensors and control strategies are selected and designed. Before the device is finally built and the control implemented, thorough work should be done in simulation and rapid prototyping to verify performance and if necessary iterate within the design process. Finally the device is built and verified. Apparently there is huge number of design parameters that needs to be fixed before a final design is achieved, and hence design optimization becomes a difficult problem. In addition to the direct specifications it is important to consider other design criteria towards a good design. Such criteria can include: (1) uniformity of force/torque performance over the workspace; (2) uniform sensitivity towards input motions; (3) uniformity of stiffness; (4) minimum inertia of structure, transmission and actuation; and (5) minimum footprint/size to workspace ratio. The ultimate goal of the methodology research is an
optimization methodology where these criteria can be balanced to achieve an overall good design. A. Conceptual design phase In this work we report mainly on the conceptual design phase. Since our applications require a stiff device we use parallel kinematic structures as a base for the work. In this phase, the “tools” to be used are MBS (Multi Body Simulation) and analytical analysis based on kinematic models of the evaluated structures, where in this paper design, modeling and analysis with an MBS system (ADAMS [16] in our case) are presented. In a first step a review of existing structures and devices is made [7]. Based on this, three candidate structures are selected and further analyzed. The following steps are considered in the design and analysis: •
Scale the selected concepts to fit within a specified volume
•
Perform a first rough calculation of the total workspace, and adjust parameters if needed
•
Select a first preliminary location of operating workspace for the device.
•
Analyze the required performance of actuators in terms of force and/or torques
These steps cover the first part of the conceptual phase of the design. The second part involves kinematic modeling e.g. to perform singularity analysis for the workspace and also to optimize the structural parameters to balance some of the different design criteria mentioned above. III.
CONCEPTUAL DESIGN AND KINEMATIC STRUCTURE
A. Specifications and design criteria The specifications given here have been obtained in dialogue with a tentative user, in this case a brain surgeon. It should be noted that it is difficult to obtain specific requirements since the application domain is completely new and unique. The specifications should hence be treated as preliminary and as giving a rough estimate for a first prototypical design. From a qualitative perspective the specifications give however a good enough starting point. The initial requirements for the new haptic device are given below •
The device should have 6 actuated degrees of freedom
•
The whole device should fit within the space of 250x250x300 [mm]
•
The translational workspace should be a minimum of 50x50x50 [mm] with no singularities within that space.
•
The rotational workspace should be +40 degrees in all directions with no singularities within that space
•
The stiffness of the device including actuation and control should be a minimum of 50 [N/mm]
•
The TCP force and torque performance should be at least 50 [N] and 1 [Nm] respectively.
IEEE-International Conference on Mechatronics, ICM 2009 Malaga, Spain •
It should be possible to place it on a table in front of the operator, easy to access for the user.
B. Geometry of the structures Three candidate mechanisms (concepts) were considered for the structural analysis and comparison of performance parameters. The first concept is a variant of the Stewart Gough mechanism [4, 7]. This concept is a 6-DoF kinematic structure, where the base is connected with six parallel legs to a moveable platform via universal, spherical and translational joints as shown in figure 1. The linear motions are achieved by linear actuators (active joints) located on the base, while the universal and spherical joints that connect the platform to the base intermediate links and linear actuators are kept passive. . Fig 3. Kinematic structure of the third concept, TAU2. The second concept TAU1 consists of three working arms connecting a fix base to the moving platform via intermediate links, by using rotational, universal and spherical joints. This structure is more complicated than the previous one and the motion of the platform or tool center point (TCP) is in this case controlled by five rotational actuators at the active joints.
Fig 1. Kinematic structure of the first concept.
The third concept TAU2 consists of three working arms with a back support arm connecting a fix base to the moving platform by using rotational, universal and spherical joints. The back support arm is provided to increase the overall workspace and making the structure more stable by counter balancing the platform inertia. The platform motion is here actuated by six motorized rotational actuators as shown in figure 3. IV.
MODELING AND ANALYSIS OF THE SELECTED STRUCTURES
The next step after selection of candidate kinematic structures is to develop simulation models of these concepts for further analysis. The concepts were modeled using ADAMS [16] MBS software as a main tool. Modeling of all the concepts followed the main steps given below: •
Scaling and configuring the model to fit in the same virtual box with the size of 250x250x300 [mm] in the modeled normal position of the mechanism.
•
Applying constraints and limits to the joints.
•
Analysis of the outer boundary of the workspace.
•
Selecting a suitable location and orientation for an assumed wanted workspace of 50x50x50 [mm].
Fig 2. Kinematic structure of the second concept, TAU1.
•
The second and third mechanisms are from a fairly new family of unsymmetrical parallel kinematic structures called TAU shown in figure 2 and 3. These mechanisms are variants of structures investigated in earlier research and student projects [2, 3].
Analysis of how much the TCP can rotate in all eight corners of the cubic workspace (applying a torque or rotation at TCP).
•
Analysis of what force or torque is required by the actuators for a wanted force/torque capacity in all six degrees of freedom (by applying a force or a torque at TCP).
IEEE-International Conference on Mechatronics, ICM 2009 Malaga, Spain A. Workspace analysis To analyze the workspace we have used an approach with two main components: •
A vector force assigned to TCP, forcing it to sweep the outer workspace boundary in X, Y and Z direction.
•
Defining restrictions on allowed actuator translations in case of the first concept and on allowed rotations for the TAU concepts to obtain realistic movements of the arms in the mechanisms.
in a similar way as for concept 1. The results from the rotation analysis at the identified most favorable position of arm 3, which is when it is oriented -40 degrees compared to arm 2, showed that the rotations around X and Z directions are good, at least +50 degrees in all eight corners, when rotating one axis at a time. The Y axis is not possible to control with this structure as earlier mentioned.
Concept 1: The first model provides six actuated DoF. The translational workspace provided by the model in X and Z directions is + 55 [mm] and along Y-direction from 260 [mm] to 350 (90 [mm]) as shown in figure 4. The maximum rotational workspace of concept 1 was determined by selecting a cube (50x50x50 [mm] according to specification) within the reachable translational workspace. Analyses were performed at each corner to determine the maximum possible rotation without violating the restrictions. The results show that the TCP provides maximum rotation when it is rotated around one axis. In case of applying rotation around multiple axes, the range of rotation of TCP is decreased. Also it is noted that the range of rotation is similar at lower corners 5, 6, 7, 8 and it amounts to +40 degrees in X,Y,Z direction while the combined rotations amounts to +35 degrees in lower corners. The combined ranges of rotation at the upper corners 1,2,3,4 are smaller than at the lower corners due to the upper stroke limits of actuators, and it is range of + 20 degrees.
Fig 5. 3-D Translational workspace of TAU1 (upper) and TAU2 (lower). Concept 3: TAU2
Fig 4 3-D Translational workspace for concept 1. Concept 2: TAU1 The TAU1 model as depicted in figure 2 provides five actuated DoF. To meet the specification, an extra rotational degree of freedom (around the Y-axis) must be attached to the moving platform. This is however excluded from this analysis. Analysis of the translational workspace of TAU1 gave the values of + 85[mm] in X-direction, + 130[mm] in Y-direction and from 0 to 170 [mm] in Z-direction, (see figure 5). The maximum rotational workspace of concept 2 was investigated
The TAU2 model provides six actuated DoF motion at the TCP. The translation workspace provided by the model in Xdirection is + 85[mm] and Y-direction is + 80[mm] and along Z-direction from 100 to 300 (200[mm]) as shown in figure 5. The results from the rotation analysis at the identified most favorable position of upper arm 3, which is when it is oriented 10 degrees above horizontal plane, showed that the rotation angles for X and Y axes are +52 degrees in all eight corners, when rotating one axis at a time. While in combination the range of rotation is decreased to + 30 degree in all the corners. Around the Z-axis the structure can provide rotation up to + 40 degrees.
IEEE-International Conference on Mechatronics, ICM 2009 Malaga, Spain B. Required forces and torques for the actuators Two different approaches were applied to analyze the force and torque requirements on the actuators for all the three concepts. The first approach is only considering the corners of the cube (50x50x50 [mm]), as targeted workspace, for the analysis. The TCP was positioned at each corner where a force 50 [N] and torque 50 [Nmm] in X,Y,Z direction were applied. The actuator forces and torques that are required to keep the TCP at that specified location were analyzed, by locking the actuator and checking the reaction forces on the actuators. For the first concept the result shows that translation of the TCP required higher forces in all X, Y, Z-direction while for rotations of the TCP low forces are required. It is also observed that similar forces are required for actuators 1 and 6, actuators 2 and 5, actuators 3 and 4 respectively. Also, the force demand on actuators 6 and 1 are higher as compared to the other, particularly in the upper corners. For the TAU1 model, the analysis of torque that is required on actuators, shows that the lower ring actuator (see figure 2) requires highest torque capacity, about 10.2 [Nm], while for arm 1 and arm 2 we can use smaller actuators (max torque ca 1.6 [Nm]). This is also good because the motors at the rings are placed in the fixed part of the structure while the smallest motors (arm 1, arm 2) are placed on the moving part of the system. It should however be noted that corner 1 requires a quite high torque for arm 2, indicating that this is a weak spot in the current workspace (detailed results are shown in [2]). For the third concept, TAU2 this first analysis approach has not been applied yet but is planned for the near future In the second approach for analysis of actuator forces and torques a more thorough investigation of the selected workspace was carried out. The approach being used, was to move the TCP in the X-Z plane along a circular path enlarged in diameter with steps of 10 [mm] through the workspace, starting in the middle of the bottom of the cylinder. In order to span the whole workspace, this motion pattern was applied at five equally spaced layers along the Y-axis while we applied a specified force of 50 [N] on TCP, acting in opposite motion direction. The obtained reaction forces/torques at each actuator show the required force/torque for that actuator. The analysis of concept 1 shows that the value of the reaction forces measured at the active linear joints increased as the TCP moves along the specified path to the outer circle. The value of forces reach the maximum value 128 [N] on leg 1 and leg 2 that require the highest demand of forces as the TCP moves along the specified path from the bottom to the top, see figure 6. The result shows a quite similar pattern of forces for actuators 1 and 2, for actuators 3 and 6 and for actuators 4 and 5, but at different force levels. (Note: Forces can be compared to torques by defining a characteristic arm length for corresponding rotational degrees of freedom.) For the second concept, TAU1, we investigated the torque required by the actuators to move TCP along the specified path through the workspace, with the same counter-acting force as for the first concept. This showed that the motor actuating the middle ring of TAU1 required the highest torque (see fig 7), as compared to lower and upper ring. The value vary between –9.70 and 9.70 [Nm] as the TCP follows the specified path The torque analysis of the third concept TAU2 shows that higher
torque is required on the upper motorized ring as the TCP moves along the specified path. The torque requirement is maximum on the upper ring, as shown in figure 7 with a few high peaks. These peaks occur for both TAU concepts on upper motorized ring and it caused by the translation of TCP in combination of xyz direction at the outer circle. The torque maximum value is 8.34 [Nm] when the TCP reaches the outer circle and then shifts to the immediate above layer. For the lower and middle motorized rings the torque requirement is quite similar and it ranges to 7.21[Nm] and 7.49 [Nm] respectively.
Fig 6. Required actuator force for leg 6 for given load
Fig 7. Required torque of middle ring of TAU1 (upper) and on upper ring of TAU2 (lower) as the TCP moves along the specified path. V.
RESULTS AND DISCUSSION
The research work presented in this paper aims to define some basic steps towards a methodology for design, analysis and optimization of haptic devices. In addition, for the first steps of this methodology, i.e. device requirements and conceptual design, three candidate concepts based on parallel kinematic structures have been studied. The configuration of the structures of these concepts, i.e. actuator locations and structural dimensions etc has been set to fit the specification. The method being used is a combination of studying earlier work within this area [7], internal discussions in the research
IEEE-International Conference on Mechatronics, ICM 2009 Malaga, Spain team and many simulations to end up with set of reasonable configuration parameters. The next step is to optimize the structure parameters to find a somehow optimal structure. One optimization criteria that can be used is to find a uniform force distribution and a low variation of torque/force of the actuators within the workspace. The work will be continued by further analysis of force/torque actuator requirements for additional directions of the force applied at TCP. At the resulting force/torque peaks, the corresponding actuator positions/angles will be analyzed for a better understanding of potential structural parameter changes towards more uniform force/torque requirements. Also more analytical approaches will be investigated, e.g. proposed by Lee et al [8] for finding optimal design parameter. Besides optimizing the force/torque characteristics, also a number of other design criteria should be considered in structural design. During the work of analyzing our three candidate concepts the parameters being identified as interesting for defining such measures so far are; volume of the device (maximum size); reachable translational and rotational workspace; selected operational workspace; and sensitivity (joint sensor output as a function of TCP motion). We can define volume efficiency as the ratio between reachable workspace and device volume.
analyzed. The performance parameters being analyzed have covered workspace analysis and force/torque requirements to fulfill the specified TCP force/torque performance. The analysis of these concepts has so far revealed some weak spots of the TAU1 concept, causing a modification to be performed but after that modification all concepts seem to satisfy the initially stated requirements. To compare and evaluate the results from the three concepts some simple indices were defined. These indices together additional indices to be developed may serve as a starting point for structural optimization of a particular concept. REFERENCES [1]
[2]
[3]
[4]
[5]
Veff = Wr / Vdev We can also define a measure for torque efficiency, Teff, to compare concepts based on solely rotational actuators and force effiency, Feff for those based on linear actuators only, where Wop is the operational workspace;
[6] [7]
Teff = Tmax / Wop , and Feff = Fmax / Wop These measure are calculated and listed in table I for the concepts being studied, showing that TAU2 has the highest volume efficiency of all concepts and that TAU1 has the highest torque efficiency but a lower volume efficiency that TAU2
[8] [9]
[10]
Table I Indices
Veff
Teff
Concept1
0.0177
---
TAU1
0.0504
0.098852
---
[12]
TAU2
0.0694
0.084993
---
[13]
VI.
Feff
[11]
0.001304
SUMMARY
This paper presents an approach to a methodology for design, analysis and optimization of haptic devices. This approach roughly divides the design process into; device requirements; conceptual design; device design and optimization; control design; and finally building a prototype of the device. This methodology is a model based approach to the design and leads to early verification and validation of different concepts. The approach will reduce development time and cost. We have applied the first two phases of the methodology on the development of a new 6-DoF haptic device. Three candidate concepts have been investigated and
[14]
[15]
[16]
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