环状可展机构运动学分析方法及应用研究

Research on Kinematics Analysis Method and Its Application of Circular Developable Mechanisms

将Moore_Penrose广义逆理论与空间连杆机构的运动传递矩阵相结合,提出了一种多杆可展机构的运动学分析方法,利用Gan和Pellegrino方法得到了机构的运动约束方程以及约束方程的雅可比矩阵,依据雅可比矩阵的奇异性和欠秩特性,获得了机构运动参数的最小二乘解。以四杆可展机构为算例,揭示了构件的截面夹角对机构收拢角和展开角的影响规律,并获得了展开运动过程中构件间夹角的变化曲线,为环状可展机构的运动控制奠定了基础。

Combining with Moore_Penrose generalized inverse theory and the motion transfer ma- trix of spatial linkage, the kinematics analysis method of multi developable linkage mechanisms was established herein. Using the method advanced by Gan and Pellegrino, the constraint equations of motion of the mechanisms and the Jacobian matrix of constraint equations were obtained. According to the singular and rank deficient characteristics of the Jacobi matrix, the least squares solution of mo- tion parameters of the mechanisms was given. Taking the deployable mechanisms of four--bars for example, the influence law of the section angle of bar on angles of folding and spreading was obtained and the curve of the angle among bars during the movement of spreading was got, which lays the foundation for the motion control.