Mobility analysis and kinematics of the semi-general 2(3-RPS) series-parallel manipulator

• The mobility of the 2(3-RPS) manipulator is revised.
• A three-dimensional coupler platform is introduced.
• A novel forward displacement analysis is introduced.
• The infinitesimal kinematics is approached by means of screw theory.
• Numerical examples are included.

This work reports on the kinematics of a series-parallel manipulator built with two zero-torsion tangential parallel manipulators assembled in series connection. Although this mechanism has been widely studied, there are some topics that must be revised, e.g. the mobility analysis here reported shows that the robot under study is not precisely a six degrees of freedom spatial mechanism as it has been commonly considered. Furthermore, the traditional hexagonal coupler platform is replaced with a three-dimensional platform which yields a mechanism with a more general topology. The forward and inverse displacement analyses of the robot are obtained in semi-closed form solutions based on simple closure equations which are generated upon the coordinates of three points embedded to the moving platform while the input–output equations of velocity and acceleration of the semi-general series-parallel manipulator are easily derived by resorting to reciprocal-screw theory. A case study is included in order to show the application of the method of kinematic analysis.