用复矢量法建立机械设计中曲线曲率半径和曲率中心的统一计算式

ANALYTIC CALCULATION FORMULA FOR PLANAR MOTION POINT TRACE′S RADIUS OF CURVATURE AND CENTER POINT OF CURVATURE

对平面运动点的位移、速度和加速度进行了复矢量描述,并引入了复矢量点积概念.在此基础上,根据平面运动点的法向加速度等于速度的平方与曲率半径的比值的思想,给出了计算点轨迹曲率半径和曲率中心的通式、直角坐标式和极坐标式,进而将其推广到机械设计中的一般平面曲线.文中还讨论了几个有代表性的分析实例.

The paper describes the displacement, velocity and acceleration of planar motion point by complex vector, and extend complex vector dot conception. Under this base, according to the theory that vertical acceleration of planar motion point equals the ratio between square of velocity and radius of curvature, the general calculation formula, the formula in form of right angle coordinates and the formula in form of polar angle coordinates for calculating motion point tracers radius of curvature and center point of curvature are submitted. Some typical examples are discussed