基于螺旋理论的3-PPR球面并联机构的奇异性分析

Singularity Analysis For 3-PPR Parallel Spherical Mechanism based on Screw Theory

提出一种新型3-PPR球面并联机构。对于每条支链中的移动副,由于其绕球面运动的特殊轨迹,可将移动副等价转换为转动副。首先,应用螺旋理论为基础给出每条支链的运动螺旋系,然后应用修正G-K公式,分析得出机构的自由度数目;其次,利用反螺旋系的解法和矩阵理论知识,在求出3-PPR球面并联机构的完整雅可比矩阵的前提下,分析矩阵的秩,得出机构产生奇异位形的条件和奇异位形的类型;最后,根据该机构的位置正解,考虑其干涉条件,利用Matlab绘制出稳定的工作空间,进行验证。研究表明,3-PPR球面并联机构无奇异位置,具备较好的应用前景。

A new type of 3-PPR spherical parallel mechanism is proposed.Due to the mobile pair special trajectory in each branch chain,the mobile pair can be equivalent conversion for revolute pair.Based on screw theory,each branched chain motion screw system is given.The mobility of this mechanism is analyzed firstly with the amendment G-K formula,The numbers of degrees of freedom is obtained.Secondly,by using the solution method of inverse spiral system and matrix theory knowledge,under the premise of Jacobian matrix of the 3-PPR spherical parallel mechanism is solved,the rank of matrix is analyzed,the singular configuration conditions and the type of singular configuration of the mechanism are obtained.In the end,according to the forward kinematics solution and interference condition,the Matlab software is used to draw up the stable working space.Research shows that a 3-PPR parallel spherical mechanism singularity is less,and easy to avoid,has good application prospect.