IEEE TRANSACTIONS ON MAGNETICS, VOL. 35, NO. 5 , SEPTeMBER 1999
3607
Design and Control of the 3 Degrees of Freedom Actuator by Controlling the Electromagnetic Force Chang I1 Yang and Yoon Su Baek Yonsei University, 134 Shmchon-Dong, Seodaemoon-Ku, Seoul 120-749, Korea
AbstracCThe novel spherical actuator with 3 D.O.F. and its control method are proposed. The proposed 3 D.O.F. spherical actuator is composed of the rotor and the stator which have the multi-poles made with the permanent magnets and the electromagnets, respectively. The rotor can make an arbitrary orientation and a spin by interactions among multi-poles of the rotor and the stator. Also the governing equation for torque generation is derlved to control the suggested model. This model is controlled with the suggested governing equation and PD control law. The various experimental results are presented to show the validity of the proposed spherical actuator.
Fig. 1 shows the interior of the actuator. It depicts five electromagnets attached to the stator and two permanent magnets attached to the rotor. The rotor and the stator coordinate systems are identical at initial state. Five electromagnets ace located at five vertices of lower half of icosahedron. At this time, the vertex located at the center of lower half of icosahedron is excepted. In order to maintain the symmetry of the rotor, N poles of two permanent magnets are oriented outward from the rotational center. Fig. 2 shows the assembly view of the 3-D.O.F. actuator schematically.
Index Term+3 D.O.F. Actuator, Electromagnetic Force, Spherical DC Servo Motor, Spherical Motor,
B Governing Equationsfor Torque Generation Coulomb's law with respect to magnetism is
I. INTRODUCTION Various kinds of motors have been used as electric actuators which have been applied not only to the industry but also to robots or manipulators. Since these actuators have only one D.O.F. for each joint, if these are applied to a wrist joint which needs multi-D.O.F., the structure gets complicated due to many links and gears, and the reliability becomes lower. To solve these problems, the development of a novel motor which has multi-D.O.F. and small and light has been requested. Therefore, we need to study the motor that has 3D.O.F. in one joint in order to kinematically simplify the link and the gear system. Vachtsevanos and Davey controlled the rotor so that it could be set at the desired position by generating a magnetic field in the stator [l]. Kaneko et al. studied 3-D.O.F. spherical DC servomotors. They studied the torque generation of 3D.O.F. DC servomotors and explained the principle of the motion by analyzing the torque constant matrix [2]. This model could spin continuously with a maximum inclination of 15". Although the structure was simple, the method of coil winding was complex and the inclination range and the torque constants were rather limited. Lee, K-M. et al. controlled the position of rotor by using the principle of VR (variable reluctance) motor [3]. The rotor moves toward minimzing the stored energy in the air gap. They found the method for increasing the workspace kinematically [3]. In this paper, we suggest a new 3-D.O.F. motor which can maintain merits of the early developed 3-D.O.F. motor and supplement defects, and investigate the validity of it.
where m,, mz are the intensities of two point magnetic poles, r is the distance between two poles, F is the magnetic force between two poles, and it orients toward the connection line between two poles [4]. In MKS units, b=6.33x104(miH).The
unitofm,,m,is[Wb],ris[m]andFisIN]. To apply (1) to the 3-D.O.F. actuator, we should establish following assumphons. First, the magnetic poles generated from the permanent magnets and the electromagnets are assumed to be the point magnetic pole. That is, since two magnetic poles, NS, can not be separated, it is assumed that the magnet for measuring the force is so long and slim that two poles of one magnet do not affect each other. These poles are called the point magnetic poles. Second, the position of the magnetic pole is located on the geometric center of the permanent magnet or the electromagnet. Third, there are no direct effects among permanent magnets or electromagnets. The magnetic flux density, the magnetic flux intensity, etc. are not varied by effects on each other.
11. MODELING OF PROPOSED MODEL A . 3 - 0 . 0 F. Actuator with New Concept Manuscript received March 3,1999. C.I.Yang t82-2-361-2827,fax +82-2-362-2736,
[email protected] Y .S.Baek +82-2-361-2827,fax+82-2-362-2736,
[email protected],kr
Permanent magnets
Fig 1, Rotor and five electromagnets of 3 D.0P actuator
0018-9464/99$10000 1999 IEEE
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(b) Iso view (a) Top view Fig. 3. Interaction between permanent magnets and electromagnets = FNl x lq FNIx @2
+
GOI
=FNlx(lq
& = FN2 Io x (F3z + @
