含双驱动支链的2UPS-RPU并联机构雅可比矩阵

Jacobian analysis of 2UPS-RPU parallel mechanism with a double actuators branch

基于旋量理论和李群李代数方法,以4自由度2UPS-RPU并联机构为例,提出了含串联输入支链的并联机构正运动学雅可比矩阵的一种新的推导方法。首先利用指数积公式建立含串联输入支链的位置正解,得出动平台位姿矩阵,根据动平台位姿矩阵列出第2和第3支链对动平台的约束方程,通过对方程组两边微分,得出第1支链关节速度与主动关节速度的映射关系,然后代入第1支链正运动学速度关系式,得出并联机构的正运动学雅可比矩阵。最后,基于螺旋理论建立了并联机构逆运动学的完整雅可比矩阵。为机构的奇异性分析提供了理论基础。

Jacobian matrix of a lower-mobility parallel mechanism（PM） includes forward kinematics and inverse kinematics,which is important in the PM design.A new method was presented for deducing the forward Jacobian matrix of the PM with the series actuators branch by taking 2UPS-RPU as an example based on Lie groups and lie algebras. Firstly, the pose matrix of moving platform by forward analysis was established through POE formula. Then the constraint equations of the second and the third chains could be listed, and the mapping relation between the first chain joint speed and the active joints was obtained through both sides differential of constraint equations. And then the results were substituted into velocity mapping relations of the first chain with the moving platform,so,the forward velocity mapping was achieved.Finally,the full Jacobi matrix of the PM was established based on the screw theory,providing a theoretical basis for singularity analysis of mechanism.