等竞曲线的数学原理与等宽凸轮机构设计

本文提出一种等宽曲线的一般参数表达式,由此导出了等宽曲线的闭合条件,切线及曲率连续条件,凸性条件;讨论了直动、摆动两类等宽凸轮机构的设计;提出了凸轮运动规律的边界条件;证明等宽曲线上曲率不连续点处将产生加速度冲击,其避免方法是对凸轮轮廓曲线进行曲率修正。

Mathematical Principle of Constant-Breadth Curve and Design of Constant-Breadth Cam

This paper presents a general parameter-equation for the constant-breadth curve, then the close equations, the continuous equations of thetangent and the curvature and the convex equations of the curve are deduced.By this mathematical principle, the design methods of the translationcam and the oscillating cam are discussed, and the boundary equationsof the cam displacement function are put forward. It is proved that there isacceleration shock in the point with discontinuous curvature, which can beeliminated by the curvature modification.