بحث بعنوان Modeling and Analysis of a 2-DOF Spherical Parallel Manipulator

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Modeling and Analysis of a 2-DOF Spherical Parallel Manipulator
Xuechao Duan, Yongzhi Yang and Bi Cheng
1 Key Laboratory of Electronic Equipment Structure Design, Ministry of Education of China,
Xidian University, Xi’an 710126, China; yzyang@stu.xidian.edu.cn (Y.Y.); chengbi@stu.xidian.edu.cn (B.C.)
2 Collaborative Innovation Center of Information Sensing and Understanding, Xidian University,
Xi’an 710126, China
* Correspondence: xchduan@xidian.edu.cn; Tel.: +86-29-8820-3040
Academic Editor: Dan Zhang
Received: 30 June 2016; Accepted: 8 September 2016; Published: 13 September 2016

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Abstract: The kinematics of a two rotational degrees-of-freedom (DOF) spherical parallel manipulator
(SPM) is developed based on the coordinate transformation approach and the cosine rule of a trihedral
angle. The angular displacement, angular velocity, and angular acceleration between the actuators
and end-effector are thus determined. Moreover, the dynamic model of the 2-DOF SPM is established
by using the virtual work principle and the first-order influence coefficient matrix of the manipulator.
Eventually, a typical motion plan and simulations are carried out, and the actuating torque needed
for these motions are worked out by employing the derived inverse dynamic equations. In addition,
an analysis of the mechanical characteristics of the parallel manipulator is made. This study lays
a solid base for the control of the 2-DOF SPM, and also provides the possibility of using this kind of
spherical manipulator as a 2-DOF orientation, angular velocity, or even torque sensor.
Keywords: spherical parallel manipulator; kinematics; virtual work principle; dynamics
Conclusions
The kinematics of a 2-DOF SPM was elaborated based on the coordinate transformation approach
and cosine rule of a trihedral angle. Moreover, the angular displacement, angular velocity, and angular
acceleration relation between the actuators and the end-effector were determined. The dynamic
model of the parallel manipulator were established by employing the virtual work principle and the
first-order influence coefficient matrix of the manipulator. Finally, typical numerical simulations of
the 2-DOF SPM reveal the quantitative relation between the input and output in terms of angular
displacement, angular velocity, and acceleration. This preliminary result lays the foundation for better
planning motion and control of the 2-DOF SPM, and also provides the fundamental verification of the
possibility of using this kind of spherical mechanism as 2-DOF orientation or torque sensors.

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