应用微分几何的观点研究了并联机床关节空间输入向量与工作空间输出向量之间的运动学非线性特性。提出了应用并联机构正解解轨迹的曲率,对解轨迹的弯曲和等间距输入映射到解轨迹上的不等间距输出的非线性程度进行度量的方法。通过对并联机构非线性引起的插补误差的分析,给出了这种非线性曲率度量方法在涉及并联机构非线性的分析中的应用实例。以并联机床VAMT1Y为例进行了分析计算,并与正解数值算法得出的结论进行了比较研究。 From the viewpoint of differential geometry, the kinematic nonlinearity between joint space input vector and work space output vector is studied. The method of using the parallel mechanism to solve the curvature of the trajectory and measuring the degree of non-linearity of the unequally-spaced output of the solution trajectory with the curvature and the equidistance input mapped to the solution trajectory is proposed. Through the analysis of the interpolation error caused by the nonlinearity of the parallel mechanism, the application example of this nonlinear curvature measurement method in the nonlinear analysis involving the parallel mechanism is given. Taking the parallel machine tool VAMT1Y as an example, the paper analyzes and compares it with the conclusions drawn from the numerical solution of positive solution.