Abstract: Firstly,movement conditions of unfolding the whole surfaces of steel balls were analyzed.According to kinematics theory, a mathematical model on spiral line unfolding movement of steel balls was established and the unfolding trajectory equation was solved by coordinate transformations.The processes of unfolding the whole surfaces of steel balls were analyzed by MATLAB simulation,and the factors affecting trajectory density of the unfolding movements were discussed.Finally,a kind of orthogonal clamping and spiral unfolding mechanism of steel balls was designed.It is successfully applied to automatic ultrasonic testing equipment of steel balls.

Key words: steel ball, sphere surface unfolding, trajectory equation, trajectory density, unfolding mechanism, orthogonal clamping

摘要： 分析了实现钢球表面全部展开的运动条件，根据运动学关系建立了钢球表面螺旋全展开的数学模型，通过坐标变换求解出展开轨迹线的方程；利用MATLAB分析了钢球表面螺旋全展开的过程，探讨了展开运动轨迹线密度的影响因素；最后设计了一种正交夹持的钢球表面螺旋全展开机构，并成功应用于钢球自动化超声探伤设备中。

关键词: 钢球, 球面展开, 轨迹线方程, 轨迹线密度, 展开机构, 正交夹持