Determination of 6D Workspaces of Gough-Type Parallel Manipulator and Comparison between Different Geometries

TLDR: Algorithms are presented to determine all the possible locations of the center of the platform that can be reached with a fixed orientation and the inclusive orientation workspace, which shows that for robots of similar dimensions the joints layout has a large influence on the workspace volume.

Abstract: We consider in this paper a Gough-type parallel robot whose leg length values are constrained to lie within some fixed ranges and for which there may be mechanical limits for the motion of the passive joints.The purpose of this paper is to present algorithms to determine:• the constant orientation workspace: all the possible locations of the center of the platform that can be reached with a fixed orientation• thetotal orientation workspace: all the possible locations of the center of the platform that can be reached with any orientation in a set defined by three ranges for the orientation angles (the dextrous workspace is an example of total orientation workspace case, the three ranges being T [0,360] degree1)• the inclusive orientationworkspace: all the possible locations of the center of the platform that can be reached with at least one orientation among a set defined by three ranges for the orientation angles (the maximal or reachableworkspace is an example of inclusive orientation workspace, the thre...