Optimisation of potential energy for positioning fixturing locators
by Lucy Siu-Bik King, Fred Feng Ling, Anthony G King
International Journal of Computer Applications in Technology (IJCAT), Vol. 10, No. 3/4, 1997

Abstract: The bare existence of solid theory, quantification and models poses an obstacle for automatic fixturing for assembly. An analytical approach based on kinematics, force and a minimisation of potential energy method is presented here to fill a portion of this deficiency. Consider potential energy as a measure of excitability of a given physical state. The physical state considered here is the fixturing configuration of locators and clamps. It is therefore desirable to find a configuration with the minimum potential for perturbation. In this paper, a 2-level optimisation method of representing and optimising the potential of the configuration is presented: (i) finding the minimum potential for a certain configuration, and (ii) optimising all possible configurations (not using exhaustive search methods). Most research in this area has concentrated on positioning locators on parts with 2-½ D straight-edged profiles. The forces calculated at each locator were either without friction or when the static coefficient of friction (λµ_s → µ_s) is at its maximum, when positive fixturing occurs just before slippage. In this presentation, the objective function for the first level optimisation finds the lowest potential by varying λ, constrained to 0 ≤ λ ≤ 1. The objective function of the second level optimisation varies the positions of the locators. The functions are nonlinear with nonlinear constraints. A random search for global minimum method was used. The method was tested on a 2-½ D inverted bell-shaped workpart which has symmetry about its centre line. Results showed that there exists a minimum potential point over all the locator positions for a configuration, and this potential energy can be used to find that configuration, which possesses the minimum overall potential energy. This configuration was confirmed by a fixturing technician given the constraints in the proposed problem. It was also tested and verified using a Bluco Fixturing Kit. This method will be further tested on other shaped workparts and will be extended to 3-D objects.

Online publication date: Mon, 02-Jun-2014

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