Algebraic structure and geometric interpretation of rigid complex fixture systems

作者：Xiong Youlun^*; Xiong Xiaorong

来源：IEEE Transactions on Automation Science and Engineering, 2007, 4(2): 252-264.

DOI：10.1109/TASE.2006.872118

• accessibility
• approachability
• complex fixture
• rigidity constraint

The rigid complex fixture is presented as a mathematical model for the analysis and design of a fixture that contains more fingers than needed for immobilizing an object alone. But the fixture with more fingers may act in violation of the approachability and accessibility conditions. So we propose the design principle for a complex fixture: the finger set must be accessible; the distance from a workpiece to the finger set should be selected such that the workpiece can be in contact with all locators simultaneously; the clamping force should enable the workpiece to be in contact with all of the locators (approachable). Furthermore, we develop a new efficient procedure of analysis and verification in screw space based on the linear programming formulation and the geometric interpretation of the rigid fixture model. In addition, we introduce a new quantitative test for force closure, captured by a function that measures how far a fixture is from achieving force closure. Locating the table problem, as a complex fixture prototype, is investigated in detail to gain a great insight into the mathematical model and the analysis procedure for the rigid complex fixture.

• 出版日期2007-4
• 单位华中科技大学