- 學位論文
機械手指之逆向運動學求解及動態分析
Inverse Kinematics Solution and Dynamics Analysis of a Robot Finger
摘要
目前機械手指已發展多年，在業界各方面的應用也越來越廣泛，逐漸的在人類工作上占有一席之地。早期的機械手指多數為低自由度的設計，如此將侷限其使用範圍。為了改善這項缺點，使其製成擬人機械手指，但也將造成逆向運動學求解的困難。 因此，本研究針對多自由度機械手指的非線性耦合關節，提出以代數法推導其逆向運動學。首先，給予指尖位置搭配座標轉換及向量法得到兩個代數方程式，接著利用三角函數將代數方程式轉換成八階多項式，來描述耦合關節關係。為了使機械手指產生平順運動軌跡及進給速率，本研究使用即時預視動態插補器(dynamics-based interpolator with real-time look-ahead , DBLA)規劃曲線中的尖銳轉角處速度及插補點。給定指尖插補點後，為了求解多項式根，本研究使用牛頓法並給予一適當初始值進行迭代求解。接著為了求得動態方程式，利用拉格蘭法(Lagrange Method)與牛頓-尤拉法(Newton-Euler Method)進行推導並交互比對，藉此了解機械手指動態行為。最後，利用Matlab軟體進行模擬與分析，驗證推導理論之正確性與可行性。
並列摘要
Robot has been developed for many years, the application of the Robot is more and more popular. It is gradually somebody in work. Most of the design of Robot for the low degree of freedom, this will limit its use. To improve this drawback, it made anthropomorphic mechanical fingers, but also cause the inverse kinematics is difficult. In this paper, for a humanoid robot finger with nonlinear coupling joints, a approach is proposed to derive the algebraic-elimination solutions of inverse kinematics. First, the given position of fingertip with transform frames and vector-loop obtain two algebraic equation, and using trigonometric terms conversed into an eight-degree polynomial for describe coupling joints. To generate the smooth jerk-limited federate profile and interpolation points, a dynamics-based interpolator with real-time look-ahead (DBLA) algorithm is applied to plane the motion trajectory. Given interpolation points of fingertip, the iterative Newton-Raphson method with a suitable initial value for solving the roots of polynomial. In order to obtain the dynamic equation of robot finger, using Lagrange method and Newton-Euler method derivation and cross match, to understand the dynamic behavior of Robot finger. Finally, using Matlab software simulation and analysis, verify the correctness and feasibility of the theory.