A method, based on the theory of instantaneous screw axes, is presented. As well as being more direct, easier to apply and wider ranging than established techniques, the new method is capable of treating linkages with screw joints. The method may be formulated geometrically, algebraically, or numerically. The algebraic approach is used here, and four examples are given to illustrate the scope of the method.
Although many studies have been carried out to determine existence criteria for different configurations of spatial linkages, no previous publication has included results for mechanisms with non-parallel screw joints. Waldron's comprehensive results for all four-bars, exclusive of those with screw joints, suggest that the CHCH- configuration is the only one likely to lead to new mobile solutions. The present paper develops the existence criteria for this linkage, using the technique of solution of closure equations. © 1974.
Waldron, KJ 1974, 'RANGE OF JOINT ROTATION IN PLANAR FOUR-BAR SYNTHESIS FOR FINITELY SEPARATED POSITIONS - 1. THE MULTIPLE BRANCH PROBLEM.', American Society of Mechanical Engineers (Paper), no. 74 -DET-108.
Graphical techniques which ensure that a linkage of given Grashof class will be capable of passing through four precision positions without change of branch configuration are presented. The conditions given are the minimal conditions needed when the Grashof class of the solution mechanism is known.
Waldron, KJ 1974, 'RANGE OF JOINT ROTATION IN PLANAR FOUR-BAR SYNTHESIS FOR FINITELY SEPARATED POSITIONS - 2. ELIMINATION OF UNWANTED GRASHOF CONFIGURATIONS.', American Society of Mechanical Engineers (Paper), no. 74 -DET-109.
The methods given in Part 1 and by K. H. Modler are used to eliminate choices of circle points which cannot give a solution linkage of given Grashof class. It is assumed here that no means of ensuring a solution of the given class is available and that trial and error will be used. The techniques presented reduce the amount of trial and error needed.
Yeo, BP, Waldron, KJ & Goh, BS 1974, 'Optimal initial choice of multipliers in the quasilinearization method for optimal control problems with bounded controls', International Journal of Control, vol. 20, no. 1, pp. 17-33.
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An algorithm to choose the initial multipliers optimally for quasilinearization solution of optimal control problems with bounded controls and constant multipliers is Proposed. It uses diagonal matrices of weighting coefficients in the performance index of an auxiliary minimization problem. This auxiliary performance index comprises the cumulative error in the system constraints and the optimum conditions in the original cxtremization problem. The auxiliary performance index is quadratically dependent on the multipliers for given state and control functions. The resulting variational problem leads to linear Euler equations. The computational characteristics of the proposed method are demonstrated with two numerical examples. © 1974 Taylor & Francis Group, LLC.