STATIC FORCE ANALYSIS OF LOWER-MOBILITY

 PARALLEL MANIPULATORS

LI Yonggang  SONG Yimin  HUANG Tian  ZHANG Ce

(School of Mechanical Engineering, Tianjin University, Tianjin 300072)

Abstract: Different from the parallel manipulators with 6 DOFs, the limbs of the lower-mobility parallel manipulators not only transmit motion and actuation force or moment but also provide constraint force or moment for their end-effectors. However, the latter one is often neglected in the past studies on static force of this class of parallel manipulators. By making use of the theory of differential manifold, it is revealed clearly that the generalized force space of the manipulators’ end-effector consists of both actuation and constraint force sub spaces. On the basis of the above analysis, the overall mappings of generalized force between input and output of manipulator are built up by use of the principle of virtual work, which consists of actuation and constraint forces mappings, i.e., two matrices. Through investigating the condition numbers of these matrices, characteristics of actuation and constraint forces transmission of the manipulator can be obtained. Moreover, this method is unified and distinct in physics and mathematics, in which it is easy to deeply understand the essence of the static force of this class of parallel manipulators. At last, the 3-UPU parallel manipulator is used as an example to demonstrate the methodology.

Key words: Parallel manipulator Lower-mobility Static force analysis Differential manifold

CLC No: TP242

国家自然科学基金(50535010, 50675151), 国家科技支撑计划重点(2006BAF01B00)和教育部高校博士点基金(20060056018) 资助项目. Received 20060830, received in revised form 20070405