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標題: | 平面與空間串聯型機械臂彈簧靜平衡方法與彈簧效能評估 Spring Balancing Methods for Planar and Spatial Articulated Manipulators and Spring Efficiency Assessment |
作者: | 莊家維 Chia-Wei Juang |
指導教授: | 陳達仁 Dar-Zen Chen |
關鍵字: | 彈簧靜平衡,平面機械臂,空間機械臂,二次型能量表示,彈簧效能, static balance,planar manipulator,spatial manipulator,energy in quadratic form,spring efficiency assesment, |
出版年 : | 2023 |
學位: | 博士 |
摘要: | 本研究旨在探討平面與空間串聯型機械臂之彈簧靜平衡方法與彈簧效能評估。
機械臂的靜平衡可帶來許多好處,如降低驅動源負載、提高效能等,相關研究行之有年。為達靜平衡,過往文獻提出方法多運用重量塊(counterweight)或彈簧等平衡元件完成系統勢能平衡。其中彈簧靜平衡方法又可依達成手段細分多種,如使用平行四連桿、凸輪或齒輪等輔助裝置給予彈簧幾何限制,將彈簧與輔助裝置組成平衡模組,安裝於機械臂分別平衡各個桿件。然而輔助裝置可能帶來額外慣性與運動干涉等問題,故本研究提出一種無輔助裝置的系統彈簧靜平衡方法:首先透過二次型(quadratic form)能量表示式將平面機械臂重力勢能與彈簧勢能以相同之矩陣形式表示,二次型包含了包含桿件位置距離的行、列向量與剛性方陣,剛性方陣中的元素對應了與各桿件姿態相關之能量係數(即剛性),透過此表示彈簧-機械臂系統總能平衡式可簡化為剛性矩陣的總和為定值。其中彈力勢能的剛性矩陣元素為彈簧參數(包含彈簧剛性、接點長度與接點角度)的函數,故可透過調整彈簧參數完成系統平衡。彈簧接點角度決定了該彈簧是否貢獻與重力反向的平衡項,本研究依此提出最佳貢獻之彈簧接點角度準則。而為完成系統平衡,已知接角的彈簧需安排於適恰桿件之間,由剛性矩陣分布可知,欲提供與重力相對應之矩陣元素,彈簧需接地安裝,而接地彈簧(ground-connected springs)除貢獻抵銷重力之元素外,亦殘留部分需由非接地彈簧(non-ground-connected springs)平衡的多餘能量,透過安排彈簧致使矩陣中所有元素皆相互抵消則完成系統平衡。本文提出將彈簧接角納入考量之三、四桿平面串聯型機械臂重力平衡彈簧配置方法。 過往靜平衡研究多僅止於針對重力的平衡,本研究另提出可對任意方向恆定力的彈簧靜平衡方法。在某些機械臂應用情境下,機械臂需長時間承受重力以外之外力,如工業用鑽頭、研磨機械臂在長加工路徑過程中需長時間承受機械臂末執行端(end-effector)與工件間的反作用力,若將該力平衡可帶來前述降低驅動負載等好處。為此,本研究首先提出任意方向恆定力的二次型能量表示式,將恆定力對於一假定之零勢能面的勢能改寫成與前述二次型重力勢能表示式相同之型式,改以此做為彈簧之平衡標的,如同機械臂的彈簧重力平衡法,透過調整彈簧配置與接點及彈簧配置安排可建立任意方向恆定力的彈簧靜平衡方法。 彈簧靜平衡方法係以複數根彈簧共同完成平面機械臂的平衡,而已知彈簧除貢獻能量用於平衡外,亦可能殘留需由其他彈簧平衡的多餘能量,若能降低多餘能量占比,則可定義該彈簧被有效使用,於此概念之下,本文建立了彈簧效能之評估方法,並進一步分析造成多餘能量的彈簧參數,藉此提出提高效能之彈簧安裝調整方法。 除上述平面機械臂靜平衡理論,本研究進一步探討空間串聯型機械臂的靜平衡。依循前述平面機械臂的平衡方法,將二次型能量表示式拓展應用於空間串聯型機械臂。相較平面機械臂,空間機械臂涵蓋三個平面的旋轉,為此本文重新建立機械臂模型,並改寫二次型中描述桿件姿態的行、列向量,納入機械臂桿件之空間向量。如同前述平面機械臂的靜平衡,透過調整空間機械臂上之彈簧接點即可達成系統靜平衡,本文基於此提出彈簧安裝準則,及三、四桿空間串聯型機械臂之重力平衡彈簧配置。 This paper proposed the spring-balancing methods of planar and spatial articulated manipulators. And the spring efficiency assessment of the spring system. The technology of static balance for physical mechanisms has been widely used for decades. It offers several advantages that have been discussed in the literature, such as decreasing the loading of actuators and improving machine efficiency. Many of the past studies use counterweights or elastic elements such as springs to achieve balancing. Among them, the spring static balance method can be further divided into various approaches. By using auxiliary devices such as parallelogram mechanisms, cams, or gears to impose geometric constraints on the springs, thereby forming balancing modules. Attaching the balancing modules on the manipulator, static balance can be achieved. However, the auxiliary devices may bring defects such as extra inertia and motion interference. To address these issues, on the explicit premise that eliminate the need for auxiliary links, we have developed a spring balancing method based on the quadratic form was proposed. The energy representation in quadratic form is composed of the stiffness matrix and the column matrix. The components of the column matrix denote the link’s distance, and the stiffness matrix components represent the energy change due to the manipulator's posture, i.e., stiffnesses. The gravitational energy and the springs’ energy are changed due to the movement of manipulator’s links, they can both be represented in quadratic form. Thereby, the balancing of the spring-manipulator system can be simplified as the summation of stiffness matrices that remain unchanged. In the gravitational stiffness matrix, the components are functions of the manipulators’ parameters (includes the link mass, distance of centers of mass, and the length); and the springs’ stiffness matrix components are functions of spring parameters (includes the spring stiffness, spring attachment distance and attachment angles). Therefore, by arrangement of the spring parameters to make the springs’ stiffness matrix components canceled the gravitational stiffness matrix components out, balancing of the manipulator can be achieved. Our study finds that the spring attachment angles determines whether the components contribute to balance of gravity, the criteria of spring attachment angles are proposed. And the rules of spring installation and the admissible spring configurations for planar articulated manipulators are proposed. In addition to balancing of gravity, we also developed a method to balance the forces in arbitrary directions. In certain applications of manipulators, they are required to withstand external forces other than gravity. For example, in drilling or grinding processes, the robotic arm needs to sustain the reaction forces between the end-effector and the workpiece along a long processing path. Balancing these forces can bring the benefits, such as reducing the load on the actuators. The potential of a constant force can also be represented in the quadratic form. Similar to gravity balancing, the forces in arbitrary directions can be balanced by arranging spring in specific angles. Our approach using multiple springs to balance the manipulator systematically. It is known that the springs not only contribute energy for balancing but may also retain a part of excess energy that needs to be balanced by other springs. If the proportion of excess energy can be reduced, it can be defined as effective utilization of the spring. With this concept in mind, this paper establishes a method for assessment of spring efficiency. We further analyze the spring parameters that contribute to excess energy, and an adjustment method for improving efficiency in spring installation is proposed. The aforementioned findings are only applicable to planar articulated manipulator, because the quadratic form representation contains the polar angles, which can only describe the links’ direction on a plane. To extend its applicability to spatial manipulators, we have reformulated it using local coordinates to describe the manipulator's posture in space. The improved quadratic form can be applied to both planar and spatial manipulators, unifying energy representations of articulated manipulators. And similar to the planar articulated manipulator, by arranging the springs to maintain a constant summation of matrices, energy balance is achieved. Our paper for the first time developed the balancing method of a spatial articulated manipulator that eliminate the needs of auxiliary links. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/90666 |
DOI: | 10.6342/NTU202300923 |
全文授權: | 同意授權(限校園內公開) |
顯示於系所單位: | 機械工程學系 |
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