不同彈簧配置下的靜平衡操作器的端點變形量分析

Abstract

在過去的研究中，串聯式操作器的力分析與末端點變形量已有充分的討論。然而對於完美靜平衡的彈簧靜串聯型操作器，因彈簧力未知使力的分析尚有探討空間。 彈簧力可以被表示為安裝於其前、後接桿件上的安裝角度和與彈簧所跨接桿件方向的分力。彈簧安裝角度與安裝位置的選擇必須滿足接頭上的力矩平衡。 接頭作用力為從末端桿開始累積在接頭上重力方向和與桿件反向之力的合力。為了滿足平衡條件，彈簧力的分力與重力或桿件方向相反，使彈簧所橫跨之接頭上的作用力降低。當調整彈簧的安裝位置與彈簧力大小，也能完全抵消與彈簧其中一個連接桿反向的接頭作用力。 作用於桿件上不平形於桿件的力也會對桿件產生變形。桿件的變形量是由桿件自身變形量以及其前接桿遞延造成變形角度累加而成。對一個從地桿到末端桿，桿長比例逐漸變短的操作器而言，與地桿連接的桿件所造成的變形量最具影響。若要降低操作器末端點的變形量，可以透過改變與地桿連接的桿件上的彈簧安裝位置、以相反方向的彈簧力來降低桿件後接點上所受到的作用力來達成。 以一個三自由度的機械手臂為例，對安裝彈簧前後的接頭作用力與末端變形量進行比較。在安裝彈簧靜平衡機構後，由於桿二的變形量降低，末端桿的變形量相較無安裝彈簧時下降了98.07%。

Force and end-point deflection analysis of serially connected manipulators are thoroughly discussed in the past. However, the analysis of spring statically balanced manipulator in perfectly balanced conditions is not widely addressed since the directions and magnitudes of spring forces are undetermined. Spring forces are represented as resultant of forces in the directions of attachment angles on pre-attached and post-attached links and links spanned. Attachment angles and lengths are selected under the constraints derived from the torque balance on the pre-connecting joints of typical links determined inwardly from end-link. Joint reaction forces are represented as resultant of gravity and forces in the directions of links iterated from the end link. Satisfying the balance conditions, joint reaction forces are reduced by forces of springs spanning across. The attachment angles of these springs are in the opposite directions of gravity or links. By adjusting the attachment lengths and magnitude of a spring, reaction forces in the direction of one of its attached links can be fully eliminated. Deflection of a typical link is a function of positions and magnitudes of forces. For a manipulator with homogeneous link properties with descending link ratio, the propagation of deflection due to the rotation angle accumulated from the ground-connecting link affects deflection on the end-point of the manipulator the most. By adjusting the attachment lengths of springs attached to link 2, joint reaction forces non-parallel to link 2 can be reduced and deflection due to forces in the direction of gravity can be compensated. Thus, end-point deflection can be reduced. An illustrative example of a 3-DOF manipulator shows the joint reaction forces and end-point deflection with/without springs is represented. With the reduction of deflection due to link 2, the end-point deflection of the manipulator is reduced by 98.07% with the installation of spring balance mechanism.