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2 April 2004 Loop closure theory in deriving linear and simple kinematic model for a 3-DOF parallel micromanipulator
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Various types of micro-motion devices have been developed in the past decade for applications including the manipulation of cells in micro-surgery and the assembly of micro-chips in micro-assembly industries. Most of the micro-motion devices are designed using the compliant mechanism concept, where the devices gain their motions through deflections. In addition, closed-loop parallel structures are normally adopted due to better stiffness and accuracy compared to the serial structures. However, the forward kinematics of parallel structures are complex and non-linear; to solve these equations, a numerical iteration technique has to be employed. This iteration process will increase computational time, which is highly undesirable. This paper presents a method of deriving a simple, linear and yet effective kinematic model based on the loop closure theory and the concept of the pseudo-rigid-body model. This method is illustrated with a 3 DOF (degree-of-freedom) micro-motion device. The results of this linear method are compared with a full kinematic model for the same micro-motion system. It is proved that the derived kinematic model in this paper is accurate and the methodology proposed is effective. The static model of the micro-motion device will also be presented. The uncoupling property of the micro-motion systems, based on the static model, will be briefly discussed.
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Yuen Kuan Yong, Tien-Fu Lu, and Daniel C. Handley "Loop closure theory in deriving linear and simple kinematic model for a 3-DOF parallel micromanipulator", Proc. SPIE 5276, Device and Process Technologies for MEMS, Microelectronics, and Photonics III, (2 April 2004);

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