四维坐标至三维坐标的转换方法研究

Research of the Transfer Method of Four-dimensional Coordinate to Three-dimensional Coordinate

在精密测量中,经常使用带旋转转台的坐标测量机。由于误差评定要求测量点必须在同一坐标系下,但测量过程中转台旋转改变了工件坐标系,因而不易进行误差评定。为此建立了一个四维坐标系到三维坐标系变换的模型,通过坐标系变换算法,利用转台坐标系作为中间坐标系,将四维坐标测量点经坐标系变换至三维转台坐标系,然后再将转台坐标系变换到工件坐标系或者机器坐标系,从而实现误差评定。实验结果表明,数学模型正确,可以满足精密测量要求。

The coordinate measure machine（CMM） with rotary table is often use in the field of precision measurement.Because of the error evaluation requires that all measured point must be expressed in the same coordinate system,but the workpiece coordinate system is changed in the process of measuring because of rotation of rotary table,so it is difficult to evaluate errors.Therefore,a model for coordinate transfer from four-dimensional coordinate system to three- dimensional coordinate system is created.Through the transfer algorithm of coordinate system,the four- dimensional coordinate with rotary table can be transferred to a three dimension Cartesian coordinate by utilizing rotary table coordinate system to act as medial coordinate system,then,it can be transferred to workpiece coordinate system or machine coordinate system,sequentially,the error evaluation is realized.The experimental results show that the mathematical model is right,and it can meet the requirement of precise measurement.