Kinematic error modeling and analysis of the loading device based on multi-body theory and stream of variation theory
Because of some reasons such as machining error and assembly clearance, the loading device will produce kinematic error during movement. While kinematic error will have a great significance on the position accuracy of the loading device. For the above reasons, firstly, the topological structure of the loading device was described based on lower body arrays. The kinematic error matrices of adjacent parts in the loading device were obtained by multi-body system kinematic theory and homogeneous translation matrix (HTM). Then an improved error modeling method was put forward, which combined multi-body system theory with stream of variation theory. And the kinematic error model of the loading device was set up with this method. Numerical results could clearly display the error transformation and propagation among components. Finally, the effect of every kinematic error on final deviation was analyzed, and error sources of a greater effect on the final deviation were obtained. This method can provide a theoretical basis to improve the accuracy of the loading device.
Dynamics of multi-body systems
The dynamic equations of multi-body systems in the form of open chains are derived by applying the principles of linear and angular momenturn to each individual member in the chain. This results in the appearance of constraint forces and torques in the dynamic equations. Using more or less classical approach these unknown forces and torques can be eliminated. Another approach is to approximate these forces byelastic and viscous forces by allowing small violations of the constraints. The well-known elimination procedure leads to a small densely coupled system of equations while the lesser-known procedure of approximating the constraint forces and torques yields a large but less densely coupled system. Both these procedures are first explained in the context of a single rigid body and then applied to a system of rigid bodies in an open chain where each body is coupled directly to at most two neighbours.
On multi-rigid-body system dynamics
Abstract A computer-oriented method for obtaining dynamical equations of motion for large mechanical systems or “chain systems” is presented. A chain system is defined as an arbitrarily assembled set of rigid bodies such that adjoining bodies have at least one common point and such that closed loops are not formed. The equations of motion are developed through the use of Lagrange's form of d'Alembert's principle. The method has been applied with human-body models and finite-segment cable models. The numan-body models are configured to simulate a crash-victim. Results obtained with several deceleration profiles agree very well with available experimental data.