雙關節四自由度機械手臂之研究

Abstract

機器人的發展源自1950年，而機械手臂今日已廣泛運用在工業上及日常生活中。本研究將汽車的傳動機構應用在機械手臂的關節，此設計使關節得以快速往返的運動。首先從正向運動學分析，利用Denavit-Hartenburg轉換矩陣，由已知的各關節轉動角度，求得在三度空間機械手臂末端的位置座標。再來利用Lagrange equation推導運動方程式，其中廣義座標包含機械系統的剛體位移，以及電機系統的線圈電流，而馬達力矩即為廣義力。推導出Lagrange equation之後，執行符號運算，以協助冗長運動方程式的推導，給予方程式右邊的力矩數值之後，呼叫ODE45，解得的曲線證實三個馬達的轉速差，能夠控制肩膀關節的兩個轉動自由度角度，並且比較不同力矩時馬達及關節的轉動情形。

Robot was invented in 1950s. Robot arm is widely used in industry and daily life. This research applied the transmission mechanism to control the joint movement of robot arm. This design effectively decelerates and accelerates joints through speed difference between motors so that the robot arm can swift back and forth quickly. The research begins with kinematic analysis. The wrist location in the space is determined by Denavit-Hartengerg notations when rotation angles at joints and displacements between links are known. This study in turn emolys Lagrange’s equation to derive equations of motion and hence construct the relationship among motor currents, rotation angles and angular velocities. Generalized coordinates include rigid body displacements in mechanical systems and coil currents in electrical systems. Generalized torque means motor torque. Because of the complexity of equations, this study used MATLAB for symbolic computing. When the Lagrange equations are derived, the numerical data of motor torques are introduced in the right-hand side of the equations. The ODE45 solver is used for the system of differential equations. When the equations are solved, the plots of results show the difference of angular velocity of threee motors can control displacements of shoulder joint in two different directions.