Description and kinematic analysis of a planar micromanipulation system based on flexure joints

This paper addresses description and kinematic analysis of a micromanipulation system based on revolute typeflexure joints. It is a five-bar planar parallel manipulator dedicated to applications requiring micro/nano scale motion. The forward kinematics problem is formulated and then solved by employing two separate approaches; (i) linearising the trigonometric functions (TF) and (ii) employing an approximate method based on linearising generalised velocity relationship for small joint space and Cartesian space displacements. Further, the velocity of the manipulator in Cartesian space is determined and compared to the results obtained from (i) linearising TF in the Jacobian matrix and, from (ii) using a constant Jacobian matrix. Numerical results prove that linearising TF in the kinematics equations and Jacobian matrix gives results close to the exact results. Using a constant Jacobian approach for analysing kinematics of micromanipulation systems contradicts the order of accuracy expected from such systems.