一种全站仪免置平实现的刚体六自由度测量方法

Rigid Body 6-DOF Measurement Method Realized by Total Station without Leveling

刚体六自由度是机械系统重要参数,其测量既可应用于运动学与动力学理论模型的验证,也可作为已知条件求解系统的约束反力等动力学分析。针对目前六自由度测量对仪器需求高、操作复杂的问题,提出一种基于常规测绘仪器全站仪实现的世界坐标系下刚体六自由度的测量方法,特点是通过全站仪测量分别设置在世界坐标系(World coordinate system,W系)和刚体的体坐标系(Body coordinate system,B系)一组已知控制点,即可实现刚体六自由度的测量,而且测量过程中全站仪无须置平操作。论文基于矩阵分析法分析了本全站仪免置平测量六自由度方法的原理,提出了数学模型并通过最小二乘法和奇异值分解相结合,实现模型的解算,在此基础上提出了本方法完整的应用步骤。利用SGT320E型三轴多功能转台与KTS460RM全站仪对本文方法进行了试验验证,并进行了相关误差分析。结果表明,全站仪免置平实现的刚体六自由度测量所得欧拉角精度(按Z-Y-X旋转顺序)分别为2.738°、3.424°、2.344°;刚体质心位置精度(按X-Y-Z顺序)分别为0.006 m、0.013 m、0.009 m,证明全站仪免置平测量方法理论和实践应用的可行性,可以满足多体机械系统中刚体六自由度的测量需求。

The 6-DOF of rigid body is an important parameter of mechanical system. Its measurement can be applied to the verification of the theoretical model of kinematics and dynamics,and it can also be used as the dynamic analysis of the constraint reaction force of the known condition solving system. Aiming at the problem of high demand and complicated operation of the current 6-DOF measurement,a method for measuring the 6-DOF of the rigid body in the world coordinate system based on the total station instrument of the conventional surveying instrument is proposed,its characteristics are as follows:the six-degree-of-freedom measurement of rigid bodies can be achieved by total station’s measuring a set of known control points in the world coordinate system(W coordinate system) and the body coordinate system(B coordinate system). and the total station does not need to be leveled during the measurement. Based on the matrix analysis method,the paper analyzes the principle of the 6-DOF method for the measurement of the total station,and proposes a mathematical model and combines the least squares method with the singular value decomposition to solve the model. Based on this,The complete application steps of this method. The SGT320E three-axis multi-function turntable and KTS460RM total station are used to verify the method,and related error analysis was carried out. The results show that the Euler angle accuracy(in the Z-Y-X rotation order) of the rigid body six-degree-of-freedom measurement by the total station is 2.73°,3.424°,2.344°,and the rigid body centroid position accuracy(in the X-Y-Z order) is 0.006 m,0.013 m,0.009 m,which proves the feasibility of the theoretical and practical application of the total station without leveling measurement method,and meet the measurement requirements of the 6-DOF of rigid body in multi-body mechanical systems.