Type synthesis of 2T1H parallel mechanisms without helical joints based on analytic formulation of screw type terminal constraints

The type synthesis of 2T1H PMs without helical joints has not been carried out in the field of mechanisms. In this paper, we propose an analytical based approach combining solving vector equations and screw theory for the type synthesis of 2T1H PMs without helical joints. Firstly, the conditions of the terminal constraints for constructing the 2T1H PMs are analyzed based on the freedom and constraint space and screw theory. Secondly, the limbs suitable for constructing 2T1H PMs are screened and determined. Thirdly, the assembly conditions for 2T1H PMs are obtained from the analytical expressions of the corresponding terminal constraints and a series of novel PMs are synthesized through the synthesis process. Finally, the kinematics of a novel 2T1H PM is analyzed and the pitch characteristic of its terminal constraints is revealed. The research provides an effective method for the type synthesis of PMs with screw type terminal constraints and motions. The proposed new mechanisms will enrich the configurations of existing PMs.