Singularity Free Workspace Aimed Optimal Design of a 2T2R Parallel Mechanism for Automated Fiber Placement

Abstract

This paper introduces a new concept of applying a parallel mechanism in automated fiber placement (AFP) for aerospace part manufacturing. By investigating the system requirements, a 4DOF parallel mechanism consisting of two revolute–prismatic–spherical joints (2RPS) and two universal–prismatic–spherical joints (2UPS) limbs with two rotational (2R) and two translational (2T) motions is proposed. Both inverse and forward kinematics models are obtained and solved analytically. Based on the overall Jacobian matrix in screw theory, singularity loci are presented and the singularityfree workspace is correspondingly illustrated. To maximize the singularityfree workspace, locations of the 2UPS limbs with the platform and base sizes are used in the optimization which gives a new design of a 4DOF parallel mechanism. A dimensionless Jacobian matrix is also defined and its condition number is used for optimizing the kinematics performance in the optimization process. A numerical example is presented with physical constraint considerations of a test bed design for AFP.