多自由度靜平衡鉸接式機械手臂彈簧安裝參數拘束規則

Constraint Rules for Spring Installation Parameters of Multi-DOF Statically Balanced Articulated Manipulators

楊統宇(Tung-Yu Yang)

指導教授 ： 陳達仁

國立臺灣大學/工學院/機械工程學研究所/碩士(2020年)

https://doi.org/10.6342/NTU202001885

摘要

本論文提出靜平衡機械手臂彈簧安裝參數(spring installation parameters, SIPs)的拘束規則。靜平衡機械手臂為在任何工作空間皆能保持靜力平衡之機構，本文使用零自由長度彈簧(zero-free-length springs)支撐桿件重量，將桿件重力位能與彈簧彈力位能函數轉換成剛性分塊矩陣(stiffness block matrix, SBM)表示式，用以表示出重力與彈力於各關節的相對位能，其中，彈力位能為彈簧安裝參數(接點距離、接點角度、剛性參數)的函數。若彈力與重力剛性矩陣中的非對角線子矩陣相加為零，則系統達成靜平衡：由此條件可得平衡方程式(balancing equations)。為了表示平衡所需的彈簧-桿件鄰接配置，使用彈簧配置矩陣(spring configuration matrix)以表示任意兩桿間是否有安裝彈簧，而不同的彈簧配置，會使得平衡方程式中的彈簧安裝參數式也有所不同。為了表示出所有的彈簧安裝參數拘束，本文假設一般彈簧配置為任意兩桿間皆有安裝彈簧，並討論一般彈簧配置下的局部彈簧接點距離、接點角度參數拘束通則；再討論特定配置下的局部彈簧接點距離、角度參數拘束規則。由上述規則只可得到目標彈簧與其他彈簧的局部參束拘束關係，有鑒於此，為了進一步系統性地描述彈簧安裝參數拘束關係，本文建立系統彈簧安裝參數拘束表(table of systematic SIP constraint)，整合局部彈簧參數拘束，以此表可以探討在靜平衡系統中的所有參數(包括桿重、彈簧參數)之間的拘束關係。
本文以可變負重靜平衡機械手臂為例，利用靜平衡系統中的所有參數之間的拘束關係，說明當機械手臂抓取不同重量的物件時，可使用滑塊裝置調整彈簧安裝參數以維持平衡。再根據上述的參數拘束規則、並考慮最小化受可變負重拘束的彈簧安裝參數數量的條件，發展出只含單一可調裝置之新彈簧配置。

關鍵字

靜平衡 ； 剛性分塊矩陣 ； 彈簧配置矩陣 ； 彈簧安裝參數

並列摘要

This paper proposed the constraint rules for the spring installation parameters (SIPs) of the statically balanced manipulator. The statically balanced manipulator is the mechanism which maintains static equilibrium in the whole workspace. In this paper, the zero-free-length springs are used to sustain the link weight. The gravitational and elastic energy are transformed into the stiffness block matrix (SBM), representing the relative potential energy on each joints. And the elastic potential energy is the function of the SIPs (including the parameters of attachment length, attachment angle and stiffness). “If the total elastic off-diagonal SBM discharges the gravitational off-diagonal SBM, the system can achieve static balance”: the balancing equations are derived according to this condition. The spring configuration matrix is used to represent if there is the spring installed between two links. And the different spring-link-attached configurations lead to the different positional arrangement of the parameters in the balancing equations. In order to discuss all the possible parameter constraints in the n-link system, the general spring configuration is set as the springs installed between any two links of the manipulators. Then the local constraint rules of the SIPs on the general spring configuration and on the specific spring configurations are derived. To know the systematic constraints of the SIPs, the local constraint rules are integrated by the table of systematic SIP constraints.
In this paper, the variable-payload manipulator is taken for example. According the derived constraint rules of the SIPs, the devices with the prismatic joints are used for adjusting the SIPs on the manipulator, which can maintain the static balance when lifting the objects with different weights.

並列關鍵字

static balance ； stiffness block matrix ； spring configuration matrix ； spring installation parameters

參考文獻

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