Screw theory-based mobility analysis and projection-based kinematic modeling of a 3-CRRR parallel manipulator

Abstract

Forward kinematics analysis of parallel manipulators requires solving highly complicated nonlinear equations, which deriving a closed-form solution is often a real challenge. Being used in closed loop position control of mechanisms, the forward kinematics solution of parallel manipulators is of great importance. Here, we investigate the mobility, forward kinematics, and inverse kinematics of a previously introduced three-degree-of-freedom spatial parallel manipulator from a new perspective. The manipulator is a 3-CRRR parallel mechanism proposed for object manipulation tasks. The mobility of the mechanism is, first, discussed using screw theory, showing that the robot has only three translational degrees of freedom. Next, the forward kinematics of the robot is analyzed based on a geometric approach. Using this method, which is the main novelty of our article, the spatial representation of the manipulator is transformed to a simpler planar representation by a projection-based interpretation, to reduce the complexity of kinematic equations. Afterward, the position of the end-effector is extracted by some algebraic expressions written based on geometrical properties of the robot. Then, the inverse kinematics of the mechanism is analyzed through the same approach. Finally, the kinematic modeling is verified using numerical and analytical methods. The results show that the obtained kinematic model has high accuracy.