基于对偶数矩阵的穿刺机器人建模及工作空间分析

Modeling Based on Dual-Number Matricesand Workspace Analysis of Puncture Robot

提出了一种穿刺机器人,由竖直移动关节、水平移动关节、前后移动关节、相互垂直方向上的两个旋转关节以及进针关节共同组成,六个关节实现对针尖姿态的调整,进而达到协助医生治病医疗的功能。阐明了一种基于对偶数矩阵建立运动学模型的整体步骤、方案,并针对所提出的穿刺机器人进行数学模型的建立,通过经典的D-H法进行验证,结果表明,用对偶数模型也能达到D-H法同样的结果,并进一步推测,假如建立一种对偶数运算法则函数,将极大提高运动学数值运算的速度,对于高关节数目的机械运动的计算具有一定的指导意义和参考价值。最后,在对偶数矩阵建立的模型基础上对机器人进行工作空间分析,初步证实了关节结构尺寸设计的合理性。

A Puncture robot is proposed,which consists of a vertical moving joint,a horizontal moving joint,a front and rear moving joint,two rotating joints in the vertical direction,and a needle joint. The six joints realize the adjustment of the needle tip posture,thereby achieving the function of assisting the doctor in medical treatment. The whole step and program of establishing kinematics model based on dual-number matrices are clarified,and the mathematical model of the proposed Puncture robot is established. The classical D-H method is used to verify the results,it is shown that using the dual-number matrices can achieve the same result of using D-H method,and further speculate,if a pair of dual-number arithmetic function is built,it will greatly improve the speed of kinematic numerical operations,and it also has a guiding significance and reference price for the calculation of many numbers of joints in mechanical motion. Finally,based on the model established by the dual-number matrices,the workspace analysis of the robot is carried out,and the rationality of the joint structure design is preliminarily determined.