可拓展至多自由度機械手臂之雙曲柄彈簧重力平衡機構

Abstract

本文提出了一種新穎的雙曲柄彈簧重力平衡機構（DSGB），該機構具有特殊的彈簧配置，用以解決其他旋轉型重力平衡器研究中觀察到的彈簧力對準與彈簧自由長度限制等問題。DSGB 可以連接到旋轉桿件或機械手臂上，以抵消其重力效應，從而實現完美的靜態平衡。 一個未平衡的接地旋轉桿件，其重力位能以二次正弦形式表示。DSGB採用雙曲柄機構，包括兩個接地的曲柄和一條穿過其端點，繞過其中一個曲柄轉軸並連接到接地彈簧的鋼纜。彈簧的伸長量為曲柄兩端之間的距離，且為一正弦函數，透過角度和幾何約束確保與重力位能的相容性。本文提出了兩種DSGB，分別為受約束中心距和無約束中心距的DSGB。為了保持重力位能和彈性位能的總和恆定，推導出彈簧的彈性常數以及與旋轉桿件之間的運動約束。將DSGB 雙曲柄的中心向量x_d軸與旋轉連桿對齊，並利用齒輪組滿足其運動約束，從而形成一個接地DSGB 模組。 本文比較了多自由度串聯式機械手臂的非接地桿件與接地桿件的重力位能，說明了接地DSGB 模組用於平衡機械手臂的可行性。更進一步提出了使用延伸地桿來確保運動約束並修改彈性常數以達到靜平衡。單自由度和二自由度範例的數值模型和軟體分析展示了 DSGB 實現完美重力平衡的可能性。 本文開發了安裝DSGB 的單自由度旋轉桿件和二自由度機械手臂的原型機，並進行了實驗研究以驗證 DSGB 的可行性和靜平衡性能。透過測量移動各關節所需的馬達扭矩，得到安裝和不安裝DSGB的單自由度旋轉桿件和二自由度機械手臂的實驗結果。結果顯示，負載0.15公斤和0.25公斤的單自由度旋轉桿件，分別安裝受約束和無約束中心距的DSGB，其平均扭矩降低百分比高達95.7%。二自由度機械手臂在相同負載和DSGB的情況下，其平均扭矩降低百分比高達95.5%。 由實驗結果得知，本文提出的重力平衡器機構DSGB可以抵銷單自由度及多自由度的旋轉桿件重力影響，並大幅降低旋轉桿件時馬達須提供的扭矩。若將此重力平衡器機構用於工業機械手臂，將會對於減少馬達輸出的功率有顯著的效果。

This paper introduces a pioneering double-crank spring gravity balancer (DSGB) with a specialized spring arrangement designed to address issues of spring force misalignment and free length constraint observed in previous studies on rotating-type gravity balancers. The DSGB can be attached to rotary links or manipulators to cancel out their gravity effects to achieve perfect static balancing. The gravitational energy associated with a ground-connected rotary link to be balanced is represented in quadratic sine form. The DSGB employs a double-crank mechanism comprising two ground-connected cranks and a cable passing through their ends, encircling one crank's pivot, and connected to a ground-connected spring. The elongation of the spring, reflecting the distance between the ends of the cranks, is formulated as a sine function, ensuring compatibility with gravitational energy through angular and geometric constraints. Two variants of the DSGB, namely constrained and unconstrained central distance DSGB, are introduced. By maintaining a constant total of gravitational and elastic energy, constraints including spring stiffness and motion compatibility with the rotary link are established. Aligning the central distance axis (x_d-axis) of the DSGB with the rotary link and ensuring motion compatibility by gear train result in a ground-connected in-line DSGB module. The paper delineates the gravitational potential energy of remote links within a multi-degree-of-freedom (multi-DOF) serial manipulator compared with that of a ground-connected link, and illustrates the viability of ground-connected in-line DSGB modules in balancing the manipulator. Modifications to spring stiffness constraints and the maintenance of motion-compatible constraints using pseudo bases for static balancing are proposed. Numerical models and software analysis for both single and double degree-of-freedom examples showcase the DSGB's capacity for perfect gravity balancing. Prototypes of both 1-DOF rotary link and 2-DOF manipulator with DSGBs has been developed, and experimental studies are held to verify the feasibility and static balancing performance of the DSGB. By measuring the required motor torque to move each joint, the experimental results of 1-DOF rotary link and 2-DOF manipulator with and without the DSGB attached is obtained. It is shown that the 1-DOF rotary link with payload 0.15kg and 0.25kg balanced by the constrained and unconstrained central distance DSGB has an average torque reduction rate up to 95.7%. The 2-DOF manipulator with the same payload and DSGBs has an average torque reduction rate up to 95.5%. From the experimental results, it is evident that the proposed DSGB gravity balancer mechanism can counteract the gravitational effects on both single-degree-of-freedom (1-DOF) and multi-degree-of-freedom (multi-DOF) rotary linkages, significantly reducing the torque required from the motor during rotation. Implementing the DSGBs in industrial robotic arms could substantially decrease the power output needed from motors.