Kumar, V. & Waldron, K. 1988, 'Force Distribution In Closed Kinematic Chains', IEEE Journal Of Robotics And Automation, vol. 4, no. 6, pp. 657-664.
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Pandy, M., Kumar, V., Berme, N. & Waldron, K. 1988, 'The Dynamics Of Quadrupedal Locomotion', Journal Of Biomechanical Engineering-transactions Of The ASME, vol. 110, no. 3, pp. 230-237.
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In the present work the design of a complex mechanical system, namely the leg of a walking machine, is investigated by using a time analysis that uses specially coded boxes to identify the use of important knowledge bases and the decisions made. Based on this study, hypotheses on the generation of sub-goals and the length of the conceptual design process are proposed for future research wotk in mechanical design theory and methods. © 1988.
Agrawal, S.K. & Waldron, K.J. 1988, 'Impulsive model for a quadruped running machine', American Society of Mechanical Engineers, Dynamic Systems and Control Division (Publication) DSC, pp. 139-148.
A model for a quadruped running machine is proposed in which controlled longitudinal and vertical impulses are delivered to the legs during support phase. A steady description of the machine is when the states at the beginning of successive cycles are invariant except for a prespecified traverse in the longitudinal direction. A graphical method is outlined to obtain steady solutions for quadruped gaits. Some representative examples of gaits are solved for the possible infinity of solutions in which a pair of feet hit the ground in unison such as the pace, bound and trot.
An investigation into the effect of the trajectory shape on resulting arm vibrations is presented based on the concept of the shock spectrum. A method to obtain trajectories whose shock spectrum has prescribed properties is briefly described, and some preliminary results are presented. A comparison of various trajectory planning algorithms, in terms of their effectiveness in reducing residual vibrations and the move time, is given. Two performance indices are defined to quantify the information obtained through the shock spectrum and the move time analysis. The superiority of a trajectory based on the simultaneous minimization of the time of travel and residual response is illustrated.
Gardner, J.F., Srinivasan, K. & Waldron, K.J. 1988, 'New method for controlling forces in redundantly actuated closed kinematic chains', American Society of Mechanical Engineers, Dynamic Systems and Control Division (Publication) DSC, pp. 315-324.
Proper control of robotic systems which incorporate closed kinematic chains is important in many applications. Among these are the multi-robot work cell and legged vehicles. In these applications the inverse problem is under-specified and hence no unique solution exists for the force distribution corresponding to a specified trajectory. A framework within which additional constraint equations may be written is presented here, and the force distribution solved in closed form for a walking machine application. These constraints are related to system performance goals of interest, such as improved traction and/or load sharing among the legs. The proposed technique is shown to be computationally simpler than other alternative solutions to the same problem.
Huang, M.Z. & Waldron, K.J. 1988, 'Efficient rate allocation algorithm in redundant kinematic chains', American Society of Mechanical Engineers, Design Engineering Division (Publication) DE, pp. 457-464.
This paper addresses a basic problem which arises in the coordination of serial chain manipulators, namely, that of decomposing a given end effector velocity state into a set of joint rates. Such a problem is indeterminate for manipulators with kinematic redundancy. A novel method of solving the rate distribution problem for the class of fully revolute-jointed, serial manipulators is developed. The technique is an extension of the axial field solution scheme developed initially for solving the force allocation problem in a statically indeterminate parallel chain system. The basis of the solution method lies in the dualities of velocity and force systems between series and parallel mechanisms. The method offers an efficient means of rate coordination and is especially useful in the control of manipulators with high degrees of redundancy. Two examples have been given for illustration.
The problem of force distribution in systems involving multiple frictional contacts between actively coordinated mechanisms and passive objects is examined. The special case in which the contact interaction can be modeled by three components of forces (zero moments) is particulary interesting. The Moore-Penrose generalized inverse solution for such a model (point contact) is shown to yield a solution vector such that the difference between the forces at any two contact points projected along the line joining the two points vanishes. Such a system of forces is described by a helicoidal vector field which geometrically similar to the velocity field in a rigid body twisting about an instantaneous screw axis. A method to determine this force system is presented. The possibility of superposing another force field which constitutes the null system is investigated.
This paper addresses the problem of the appropriate distribution of forces between the legs of a legged locomotion system for walking on uneven terrain. The legs of the walking machine and the terrain form closed kinematic chains. The system is statically indeterminate and an optimal solution is desired for force control of the legs. In addition, as unisense force limitations are imposed on the wrenches acting at the feet, it is important to be able to determine for any given configuration whether or not a set of valid contact forces can be found which will ensure the stability of the vehicle. Fast and efficient algorithms to solve these problems have been developed. The trade-off between computational simplicity and optimality makes it necessary to resort to suboptimal algorithms. In particular, schemes based on the Moore Penrose Generalized Inverse or the pseudo inverse, and linear programming were investigated. An active compliance control scheme with varying leg compliances is a suitable paradigm for control. A variation of the linear programming technique that is well-suited to the problem of predicting instability in the vehicle is also presented.
Sabada, S., Srinivasan, U., Kinzel, G.L. & Waldron, K.J. 1988, 'Automatic synthesis of four-bar mechanisms for four-position motion generation', American Society of Mechanical Engineers, Design Engineering Division (Publication) DE, pp. 121-128.
The synthesis of four bar mechanisms designed to go through four precision positions based on optimization theory and rectified synthesis are discussed. The techniques for automatic synthesis presented have been implemented in the interactive synthesis package RECSYN.
Srinivasan, U., Sabada, S., Kinzel, G.L. & Waldron, K.J. 1988, 'Automatic synthesis of four-bar mechanisms for two- and three-position motion generation', American Society of Mechanical Engineers, Design Engineering Division (Publication) DE, pp. 113-120.
A method is presented for the automatic synthesis of four bar mechanisms based on optimization theory. The procedure applies to designs for rigid-body guidance for two and three finitely separated positions of the coupler when the mechanism is driven at one of the cranks. The technique presented here incorporates rectification developed by K.J. Waldron (1975, 1977) and K.J. Waldron and R.T. Strong (1978a, 1978b, 1979), to eliminate branch and order problems and is implemented in the interactive synthesis package RECSYN (J.C. Chuang, Strong and Waldron, 1981).
In this paper we have identified aspects important to the mechanical designer at the conceptual design stage. The creation of successful CAD design tools must take these into account. These are the functionality, optimization and the language of design. The cognitive studies which support this assertion are presented.