Dimensional synthesis of a 3-translational-DOF in-parallel manipulator for a desired workspace

This paper deals with the synthesis and optimization of the workspace of a 3-translational-DOF in-parallel manipulator (3-T-P-M). Three variable length legs constitute the actuators of this manipulator, whereas two other kinematicsʹ chains, with passive joints, are used to eliminate the three rotations of the platform with respect to the base. The workspace is made of the intersection of two workspaces. The first one is relative to the active legs, called here “active workspace”, and the second one is relative to the passive chains called here “passive workspace”. The influence of the link lengths of the passive chains is discussed. Then, for a desired active workspace, the dimensions of the passive chains are determined to yield the maximum size of the platform workspace, i.e., the active workspace is not altered by the presence of the passive kinematicsʹ chains. The problem is presented first as a geometric one, in the case where the joint limits were not taken into account. Then, for the case where the joint limits were considered, the problem is presented as an analytical one. The solution was found analytically when the arm and the forearm, of the passive kinematics chain, have equal lengths. A numerical solution is then presented for the general case. The discussion is illustrated by examples showing the different cases that could arise.