Kinematic Synthesis and Analysis of a Novel Class of Six-DOF Parallel Minimanipulators

Abstract

A new class of six-degree-of-freedom (six-DOF) parallel minimanipulators is introduced. The minimanipulators are designed to provide high resolution and high stiffness in fine- manipulation operations. Two-DOF planar mechanisms (e.g., five- bar linkages, pantographs) and inextensible limbs are used to improve positional resolution and stiffness of the minimanipulators. The two-DOF mechanisms serve as drivers for the minimanipulators. The minimanipulators require only three inextensible limbs and unlike most of the six-limbed parallel manipulators, their direct kinematics can be reduced to solving a polynomial in a single variable. All of the minimanipulator actuators are base-mounted. As a result, higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained.<P>Inverse kinematics of the minimanipulators has been reduced to solving three decoupled quadratic equations, each of which contains only one unknown.<P>Kinematic inversion is used to reduce the direct kinematics of the minimanipulator to an eighth- degree polynomial in the square of a single variable. Hence, the maximum number of assembly configurations for the minimanipulator is sixteen. It is proved that the sixteen solutions are eight pairs of reflected configurations with respect to the plane passing through the lower ends of the three limbs.<P>The Jacobian and stiffness matrices of two types of minimanipulators are derived. It is shown that, at a central configuration, the stiffness matrix of the first type minimanipulator (driven by bidirectional linear stepper motors) can be decoupled, if proper design parameters are chosen. It is also shown that the stiffness of the minimanipulators is higher than that of the Stewart platform. Guidelines for obtaining large stiffness values and for designing the drivers of the second type minimanipulator (simplified five-bar linkages) are established.<P>An algorithm is developed to determine the workspace of the minimanipulators. Given any orientation for the output link, three-dimensional representation of the workspace is obtained. Guidelines for avoiding discontinuities inside of the workspace are established.<P>Necessary and sufficient conditions for both inverse and direct kinematics singularities of the minimanipulators are obtained. Guidelines for avoiding direct kinematics singularities, which occur within the minimanipulator workspace, are established.