Kinematics and Statics Analysis of a 2-DOF Planar Parallel Mechanism with over Constraint



This paper presents a deep research on 2-DOF planar parallel mechanism during developing a new type of hybrid machine tool. The composition of this planar parallel mechanism is introduced, its direct and inverse kinematics solution equations as well as the solution equations for the speed and the acceleration are deduced, meanwhile, the jacobian matrix is obtained. The statics problems of the parallel mechanism are modeled and analyzed based on principle of virtual work, and the balancing driving force solution equation of the driving part is given. Through the solving process we can see that the direct and inverse solution equations of this mechanism have explicit expressions and convenient to realize real-time control. It forms a solid basis for the design and development of this mechanism.




Jingying Zhao




X. Z. Han et al., "Kinematics and Statics Analysis of a 2-DOF Planar Parallel Mechanism with over Constraint", Advanced Materials Research, Vols. 261-263, pp. 913-917, 2011


May 2011




[1] Zhang Shu, Heisel U: Parallel Kinematics Machine Tool. (China Machine Press, Beijing 2003).

[2] Cheng Xianguo, Zhao Henghua, Gao Xingjun. Current Researches and Development of Parallel Machine Tools. Machine Building and Automation Vol. 36(2007), pp.8-10.

[3] Shen Huiping, Zhang Shu, Wang Pingling, et al. New Progress of Research Activities and Achievements of Parallel Kinematic Machine in Germany. China Mechanical Engineering Vol. 18(2007), pp.2130-2136.

[4] Gao Jinlian, Han Yingqiang, Li bo, et al. Simulative Design on the Globe Hinge of Parallel Robot. Journal of Machine Design Vol. 24(2007), pp.53-55.

[5] Bai Zhifu, Chen Wuyi. Stiffness Computation Model of Spherical Joints and PKM's Stiffness Improvement by Redundant Leg. Chinese Journal of Mechanical Engineering Vol. 42(2006), pp.142-145, 150.


[6] Liu X J, Wang J S, Li T M, et al. Parallel Mechanisms with two or three Degrees of Freedom. Tsinghua Science and Technology Vol. 8(2003), pp.105-112.

[7] Wu J, Wang J S, Li T M, et al. Analysis and Application of a 2-DOF Planar Parallel Mechanism. Journal of Mechanical Design Vol. 129(2007), pp.436-437.