This paper presents a new formulation for the equations of motion of interconnected rigid bodies. This formulation initially uses Cartesian coordinates to define the position of the system, the kinematic joints between bodies, and forcing functions on and between bodies. This makes initial system definition straightforward. The equations of motion are then derived in terms of relative joint coordinates through the use of a velocity transformation matrix. The velocity transformation matrix relates relative coordinates to Cartesian coordinates. It is derived using kinematic relationships for each joint type and graph theory for identifying the system topology. By using relative coordinates, the equations of motion are efficiently integrated. Use of both Cartesian and relative coordinates produces an efficient set of equations without loss of generality. The algorithm just described is implemented in a general purpose computer program. Examples are used to demonstrate the generality and efficiency of the algorithms.
This paper presents a numerical solution method for dynamic analysis of constrained mechanical systems. This method reduces a coupled set of differential and algebraic equations to state space form. The reduction uses an independent set of velocities which lie on the tangent plane of the constraint surface. The tangent plane is defined by the nullspace of constraint Jacobian matrix. The nullspace basis is found using QR decomposition of the constraint Jacobian matrix. Because the nullspace basis is not unique, directional continuity of the nullspace is difficult to preserve each time the Jacobiar is decomposed. This paper presents an updating algorithm that is used instead oj repeated decomposition. This preserves directional continuity of the Jacobian matrix and increases efficiency. State equations are then derived in terms of independent accelerations and therefore can efficiently be integrated. Generalized velocities are integrated with constraints to obtain positions. This method has demonstrated minimal constraint violations and improved efficiency. Numerical examples with singular configurations and redundant constraints are presented to demonstrate the effectiveness of the method.
This paper describes the development of computer-based software for three-dimensional geometric data base of the human musculoskeletal system. Using a computer graphics workstation, a user of the software will interactively display detailed information about the muscles, tendons, ligaments, bone, and joint anatomy. This software will enable a wide range of health care workers to visualize complex physiological data. In addition to geometric and visual realism, this software will include kinematic relationships which allow the calculation and display of the motion and forces of the joints, muscles, and tendons. This will permit a user to interactively move joints or tendons and display the resulting motion of the surrounding tissues, as well as internal reactive forces and joint pressure distribution. A two-dimensional version of this software is currently being used for knee and hip osteotomy preoperative planning, total joint replacement prosthesis design and dimensional selection, and osteochondral allograft sizing and reconstruction using radiographic data.
This paper presents two vehicle models used to investigate the effects of active suspensions. One is a linear seven degree of freedom ride model. The second is a nonlinear ten degree of freedom ride and handling model. Full state feedback optimal control algorithms are developed for both models. The seven degree of freedom model is used to study ride effects. The active suspension substantially reduced the motion of the sprung mass. The ten degree of freedom model is used to study the effects of the active suspension on the directional response characteristics of the vehicle. The handling characteristics exhibited by the active suspension are very similar to those of the passive suspension. However, the active suspension did significantly reduce sprung mass motions during the handling maneuvers. It is then illustrated that by altering various feedback gains, active suspensions can be made to change the handling characteristics in the nonlinear range.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.