引用本文: 陈宇航, 赵铁石, 宋晓鑫, 何勇, 李忠杰. 变结构并联多维振动台自由度特性与运动学分析[J]. 机器人, 2016, 38(2): 135-143.
CHEN Yuhang, ZHAO Tieshi, SONG Xiaoxin, HE Yong, LI Zhongjie. Analysis of DOF Properties and Kinematics for Variable Configuration Parallel Multi-dimensional Vibration Platform[J]. ROBOT, 2016, 38(2): 135-143.
 Citation: CHEN Yuhang, ZHAO Tieshi, SONG Xiaoxin, HE Yong, LI Zhongjie. Analysis of DOF Properties and Kinematics for Variable Configuration Parallel Multi-dimensional Vibration Platform[J]. ROBOT, 2016, 38(2): 135-143.

## Analysis of DOF Properties and Kinematics for Variable Configuration Parallel Multi-dimensional Vibration Platform

• 摘要: 基于 3-P（4S）构型设计并研制了一种直线电机驱动的、平衡位姿可调的变结构并联多维振动台．运用约束螺旋理论分别对子闭环初始安装为平行四边形和梯形的两种构型进行自由度特性分析．建立两种构型的运动学位姿模型，研究机构位姿输出与驱动输入的关系，通过迭代搜索法求解梯形安装时机构的非线性约束方程组．根据位姿分析，分别用反解搜索法和正解遍寻法得到两种初始安装条件下机构的可达工作空间以及梯形安装时的伴随转角空间．通过数值算例验证理论分析结果，对机构进行运动仿真，研究不同装配结构下振动台机构的运动输出特性．依据理论分析与仿真结果进行实物样机运动实验，将理论计算、仿真分析和实验的结果进行对比，进一步验证了理论分析的正确性以及样机工程应用的可行性．

Abstract: A linear motor-driven variable configuration parallel multi-dimensional vibration platform with adjustable balance pose is designed and developed based on 3-P(4S) configuration. The constraint screw theory is used to analyze the DOF (degree of freedom) properties of two configurations of which the sub closed-loops are initially installed as a parallelogram and trapezoid. Kinematic models of position and attitude of two configurations are established, the relationship between pose output and driving input is studied, and the nonlinear constraint equations of mechanism with trapezoid installation are solved by iterative search method. According to pose analysis, reachable workspace of mechanism under two initial installation conditions are obtained by using inverse solution search method and positive solution ransacking method respectively, as well as the adjoint rotation workspace under trapezoid installation. By numerical example, the results of the theoretical analysis is verified. Through motion simulation of the mechanism, kinetic output features of the vibration platform under different initial configuration are studied. Motion experiment of physical prototypes is conducted based on theoretical analysis and simulation results. The results of theoretical calculations, simulation analysis and experiment are compared, and the validity of theoretical analysis and feasibility of the prototype engineering applications are verified further.

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