Kinematic and singularity analysis of a 4-DOF Delta-type parallel robot

The research presents a kinematic analysis of a recently proposed Delta-type parallel robot with four degrees of freedom. In contrast to conventional Delta robots, the design of the proposed one allows its output link to rotate about a fixed axis. The article first considers the mobility analysis using screw theory and verifies the motion pattern of the output link. The inverse kinematics follows next and provides the relations used for a subsequent study on workspaces. All performed calculations form a basis for a singularity analysis, which constitutes the largest part of the work. To analyze singular configurations, the paper considers two approaches. The first approach operates with Jacobian matrices; the second one determines closeness to singularities by concerning actuation speeds and efforts. Both methods provide similar results, which confirms the validity of the applied techniques. Next, the paper presents an example of workspace analysis concerning constraints on the actuation efforts. The proposed method gives more accurate results compared with another conventional approach. Finally, the paper considers an example of trajectory planning between two singularity-free areas of the workspace. The developed techniques are used to move between these areas by adjusting the platform orientation.