Murthy, V & Waldron, K 1992, 'Position Kinematics Of The Generalized Lobster Arm And Its Series-parallel Dual', Journal Of Mechanical Design, vol. 114, no. 3, pp. 406-413.
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The generalized lobster arm is a six revolute open kinematic chain with 3 consecutive intersecting pairs of axes. A new solution of the inverse position kinematics problem of this arm which takes advantage of its specific geometry is presented. A compari
Song, SM, Lu, FH, Chen, NX & Waldron, KJ 1992, 'Determination of the shortest crank in four position synthesis: a numerical apporach', American Society of Mechanical Engineers, Design Engineering Division (Publication) DE, pp. 315-321.
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The shortest crank of a four position synthesis can be determined by solving a statically determinate five-bar structure and a set of seven nonlinear equations have been proposed for this purpose. In this paper a numerical method which can directly solve the shortest crank is presented. It is found that a direct implementation of the original seven equations has two problems: many spurious solutions and poor numerical stability. And the spurious solutions are of the following two types: solutions with incorrect signs of angles and solutions with incorrect geometry. In order to solve the problems, a set of ten equations is developed and parameter perturbation method is applied. Furthermore, a set of eight equations is developed for better numerical stability. Both the ten and eight equations can eliminate the spurious solutions with incorrect geometry. Yet the spurious solutions with incorrect signs of angles can only be rectified after convergence. An automatic search algorithm is included to automatically search the shortest crank in the solution space. Many examples are given to illustrate this numerical approach.
Venkataraman, SC, Kinzel, GL & Waldron, KJ 1992, 'Optimal synthesis of four-bar linkages for four-position rigid-body guidance with selective tolerance specifications', American Society of Mechanical Engineers, Design Engineering Division (Publication) DE, pp. 651-659.
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In practical rigid-body guidance problems, very often one or more of the design positions need not be generated exactly. Further, extreme accuracy at the design positions is somewhat pointless considering the inherent limitations in linkage manufacturing processes. This emphasizes the requirement of synthesis techniques to be able to handle tolerance specifications on the nominal design positions. A favorable offshoot of the tolerance incorporation would be the accompanying increase in the solution space of the synthesis problem thereby yielding better linkage solutions.