Researches On Workspace Of Planar Generalized Stewart Platform

Planar Stewart platform is a three degrees of freedom parallel mechanism.Planar generalized Stewart platform is ist extended form which consists of a fixed rigid body(the base),a moving rigid body(the moving platform or the platform)and three distance or/and angular constraints between 3 pairs of points and/or lines,points and/or points,lines and/or lines between the base and the platform.The workspace analysis of parallel mechanism is a basic work in the process of mechanism design,trajectory planning and parameters selection.It is also the basis for evaluating the working ability of parallel mechanism.This paper mainly includes the following research contents:1.According to constraints between the base and the platform,the different types of direct kinematics to planar GSP is transformed into a constraints graph by the constraints relationship between the geometry of the platform.The under-constrained constraint graph is completed to make it well-constrained and acquire a construction sequence.The equation system of each construction sequence is solved with Wu's elimination method to obtain the closed form solution.2.The simulation is performed by MapleSim software.The effectiveness of the method is verified by experiments.3.The workspace of planar generalized Stewart platform is studied based on direct kinematics of planar generalized Stewart platform,and the symbolic expression of reachable position of moving platform is obtained.The images of the workspace are drawn with Maple software.