A Conceptual and Straightforward Approach for Solving the Closed-form Direct Kinematics of a General Coplanar 6-PUS Parallel Manipulator

The proper synthesis of simulators is critical as they allow trainees to experience dangerous maneuvers. The most widely used simulator is the Stewart platform. However, this structure is costly and therefore alternative structures should be considered. The 6-PUS robot is an excellent alternative to the well-known Stewart, thanks to its inherent benefits. Considering the many existing studies on parallel robots, specifically the Stewart robot, there exists a few research on the 6-PUS structure. The comprehensive kinematic analysis of any robot is a prerequisite for robotic engineers. Therefore, to analyze the 6-PUS structure, first, a general kinematic architecture of the 6-PUS robot is defined, in which all actuators are located on a plane connected to the ground. To solve the closed-form direct kinematics, a highly computational efficient elimination method is selected and a detailed stepwise approach is presented which results in a great reduction of the univariate polynomial degree without using the greatest common divisor method. Thanks to its simplicity of implementation and straightforward approach of the presented algorithm, it is theoretically worthwhile in the kinematics analysis of robots. The presented stepwise and conceptual approach to kinematic analysis is general and can be applied to other parallel structures.