Kinematics, workspace and optimal design of a novel 4 R SS + PS parallel manipulator

Abstract

In this paper, a novel four degrees of freedom (DOFs) parallel manipulator (PM) is introduced and its kinematics, workspace and optimal design are systematically studied. The manipulator is called 4RSS\u2009+\u2009PS PM having four active RSS type legs and one passive PS type leg. R, S and P stand for revolute, spherical and prismatic joints, respectively, and R denotes the actuated revolute joints. Moving platform of the manipulator has three rotational motions along with one translational motion (3R1T). As an advantage, rotational motion of the moving platform around the axis of its translational motion has no limitation. This makes the manipulator so suitable for machining applications in holes, cylinders and so on. Closed form solutions are found for the inverse and forward position kinematics problems of the manipulator. The manipulator workspace is determined numerically in a 3D space. A special design of the manipulator free of inverse and forward kinematic singularities is specified. Kinematic dexterity analysis is carried out based on the condition number of the manipulator Jacobian matrix showing that the manipulator has no singularity inside the workspace. Two architecture optimizations are also presented to achieve a maximum workspace volume of the manipulator, and to find a workspace with a desired value of kinematic dexterity.