调平二自由度球面并联机构运动学分析与求解

Kinematics analysis and solution of leveling spherical parallel mechanism with two degrees of freedom

球面并联机构操作灵活、控制简单,尤其适合于飞行器运动模拟、光束指向控制及平台调平领域。为了提高调平效率,提出了一种适用于调平领域的球面并联机构,首先介绍该机构构型,由动平台、底座、两对称分布驱动支链及球副支腿构成。针对机构特点,基于螺旋理论分析机构自由度与约束,给出机构自由度矩阵与约束矩阵,得出该机构有2个转动自由度。依据构型建立机构坐标系,通过构造闭环矢量,建立驱动长度与动平台转动角度的数学模型并求得运动学逆解。利用3D模型进行运动学仿真,求解机构位移、速度、加速度。结果表明,所提出的机构具有较好的位移分辨率且结构简单,可作为倒装键合等调平机构的基础件,具有很好的应用价值。

The spherical parallel mechanism has the advantages of flexible operation and simple control,and is especially suitable for aircraft motion simulation,beam direction control and platform leveling field. In order to improve the leveling efficiency,this paper presents a spherical parallel mechanism applicable to leveling fields. Firstly,the configuration of the mechanism is introduced. The mechanism is composed of a movable platform,a base,two symmetrical distribution driving branched（ PSP） and a ball pair supporting leg. According to the characteristics of mechanism,the degree of freedom and the constraint of the mechanism are given based on the screw theory. It is proved that the mechanism has two rotational DOF. According to the configuration of the system,the mathematical model of the driving length and the rotation angle of the moving platform is established by constructing the closed loop vector,and the inverse kinematics solution is obtained. In addition,3D model was used to simulate the kinematics,and the displacement,velocity and acceleration of the mechanism were solved. Simulation result shows that,the proposed mechanism is easy to control and has good displacement resolution. It can be used as the basic component of the flip chip bonding mechanism and other leveling mechanism,which is of great application value.