平面铰链五杆机构的奇异性研究

Study on the singularity of a planar five-bar mechanism

推导了平面铰链五杆机构的雅可比矩阵,得出机构处于奇异位置时的姿态,并给出了避免五杆机构奇异的方法:当五杆机构雅可比矩阵的行列式det(J)=0时,可使规划的轨迹远离工作空间的边界,避免该种奇异;当五杆机构雅可比矩阵的行列式det(J)→∞时,可选择合适的机构尺寸、合适的机构位姿形式或使规划的轨迹不通过奇异轨迹避免机构奇异.开发了五杆机构奇异轨迹的仿真软件,为五杆机构的设计提供了依据.

Jacobian matrix of a planar five-bar mechanism is deduced and the posture of a planar five-bar mechanism is given when the mechanism locates in singularity position. By analyzing the determinant of Jacobian matrix det（J） of a planar five-bar mechanism, the methods to avoid singulari si si ngularity can be avoided by making the real path far from the boundary ty are presented. When det（J） = 0, of work space; When det（J）→∞, ngularity can be avoided by selecting suitable dimensions of the mechanism, by selecting suitable mechanism posture or by ensuring that the real path doesn＇t go through the singularity path. A set of software is developed to simulate the singularity path and it provides the basis for the design of a five-bar mechanism.