機械手臂關節與磁性齒輪之研究

Abstract

機械手臂主要可分為串聯式與並聯式機械手臂。雖然，手臂發展技術已日趨成熟，但兩種型式的手臂仍各有缺點。使用雙馬達來操控機械手臂，即可提昇手臂加減速之速度並改善上述的缺點。因此，本研究利用拉格蘭吉方程式推導雙馬達機械手臂傘齒輪關節的運動方程式，並解出馬達力矩與關節位移、速度和加速度之間的關係。 運用軟體模擬可驗證馬達關節與齒輪間之關係；再利用MATLAB軟體模擬機械手臂關節方程式，得知位移、速度與加速度三者存在微分積分關係。接著，執行對馬達輸入定電壓的實驗，與MATLAB模擬比較力矩、位移隨時間的變化，以驗證所推導的機械手臂運動方程式。 一般機械手臂靠著接觸式齒輪達成減速的作用，但是振動噪音大，而且存在背隙。另一型式為非接觸式齒輪如磁性齒輪，齒與齒間不會直接接觸。為了將磁性齒輪的優點應用於傘齒輪關節，本研究設計三種磁性齒輪，並使用軟體模擬、分析和比較，歸納出磁性齒輪在設計時，齒輪1和2的背鐵厚度必須大於磁鐵厚度、齒輪3背鐵應放於磁鐵下方，並且齒輪3背鐵厚度應小於磁鐵厚度，如此設計可產生較大的磁力。

Robots arm can be classified into serial robot and parallel robot. Although the technique of robot arms has become well developed, these two types still have their own drawbacks. Using dual motors to control robot arm can enhance the velocity of arm acceleration and deceleration and also improve above drawbacks. Therefore, this research uses Lagrange equations to derive equations of motion for robot joint of dual motor with bevel gear mechanisms and solves joint displacement, velocity, and acceleration subjected to motor torque. This study uses a software to verify the relation of motor joint and gears, and utilize a MATLAB software to simulate motor arm joint equation and obtain displacement, velocity, and acceleration. Then, comparing curves of torque and displacement versus time by motor experiment of input constant voltage and MATLAB simulation verifies derivation results of equations of motion for robot arms. Robot arms ordinarily use the type of contacting gear to achieve deceleration function, but this kind of gear has loud vibration noise and backlash. The other form is non-contacting type, like magnetic gears. The teeth of the gears do not have to contact directly. In order to take advantage of magnetic gears and make good use of the bevel gear joint, this research designs three types of magnetic gears and uses a software to simulate, analyze, and compare them. Simulation results show that the back irons on gear1 and gear2 should be thicker than the magnet. The back iron of gear3 needs to be put below its magnet and the back iron on gear3 should be thinner than its magnet thickness. Designs like this can produce larger magnetic force.