Workspace Analysis of a Six-legged Robot Based on Group Theory

For the complicated structure of a six-legged robot, a simplified model is proposed to transform the robot legs into slid links using the constraint under equivalent conditions. By this way, the reachable workspace and orientation workspace of the simplified model are defined based on the motion constraint equations. Then the symmetry relationship between initial states and workspace is emphatically analyzed based on the motion constraint model and group theory. To compute and quantify the workspace of the robot, a hierarchical searching method is used. By simulation data, the changes of the workspace with different parameters are analyzed, the workspaces of the robot under different initial states are compared, and the orientation workspace of the motion platform and its cross section are also shown. As shown in analysis and simulation, the workspace of complicated parallel mechanisms is analyzed in detail by a constraint model based on group theory, and the detailed information of workspace symmetry, orientation workspace and cross section is obtained.