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The planar three-degree-of-freedom (DoF) parallel mechanism plays a significant role in the fields of automobiles and electronics due to its advantages such as high stiffness, large carrying capability, and stable operation. In this paper, a planar 3-DoF (2T1R) parallel mechanism is derived by structural evolution from the parallelogram by means of Grassmann line geometry and the Atlas method. First, the position equation of the mechanism is established and the inverse kinematics and Jacobian matrix are investigated. The maximum deviation between the theory and simulation results of the inverse kinematics and Jacobian matrix is 0.48%, which verifies the accuracy of the theoretical model. Then, the constraint conditions of the mechanism are defined. Based on the inverse position solution, the numerical method is used to solve the workspace of the mechanism. It is concluded that the ratio of the workspace to the entire triangular space is about 15% higher than that of the 3-PRR parallel mechanism. Next, based on the Jacobian matrix, the performance indexes are established to evaluate stiffness and dexterity. Finally, the size of the mechanism is optimized by means of the genetic algorithm to improve the comprehensive performance.
Wang et al. (Sun,) studied this question.
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