Accurate Simulation Solutions of Euler Angular Velocity/Acceleration and Statics of Parallel Manipulators by CAD Variation Geometry

Abstract

A CAD variation geometry approach is proposed for accurately solving the Euler angles, Euler angular velocity/acceleration, and the active forces due to a concentrated torque of limited-DOF parallel manipulators (PMs). First, a simulation mechanism of PM with Euler angles, a simulation mechanism of PM with Euler angular velocity/acceleration, and a simulation mechanism of PM with Euler angular torques are created and combined into one simulation mechanism. Second, when modifying the driving dimension of the active legs, the simulation mechanism of PM is varied correspondingly, and the Euler angles, Euler angular velocity/acceleration, and active forces due to the concentrated torque are solved automatically and visualized dynamically. Third, a 3DOF PM and a 5DOF PM are illustrated, and their Euler angles, Euler angular velocity/acceleration, and active forces due to the concentrated torque are solved accurately by CAD variation geometry and are verified by the analytic solutions.