Kinematic optimization of a chopsticks-type micromanipulator

A design concept for a micromanipulator is presented. The design uses two 6-DOF platform type parallel manipulators to a set of 'chopsticks.' Each manipulator utilizes six piezoelectric prismatic actuators. The required motions of the chopsticks to accomplish some generic tasks such as grasping, positioning, orienting and applying forces are analyzed. It is shown that translational motion of the tips of the chopsticks is more important than orientational motion. The kinematics of the manipulator are derived. Because the piezoelectric actuators have very limited motion ranges, the configuration of the manipulator remains essentially constant throughout the workspace. This makes it relatively easy to analyze the workspace of the manipulator using the singular values of the Jacobian matrix. Large singular values make for a larger workspace. An optimization scheme is developed based on kinematic performance criteria (mobility and workspace shape). Some singular configurations of the manipulator are shown. Approaching one of these singular configurations allows the limited motion range of the the piezoelectric actuators to be amplified in 3 directions simultaneously. Several representative designs are shown graphically along with their workspaces.