Loop Closure Theory in Deriving Linear and Simple Kinematic Model for a 3 DOF Parallel Micromanipulator

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.