Papers by Keyword: Fully Cartesian Coordinates

Abstract: The dynamic of a type of play equipment, Big Pendulum Hammer, was modeled and simulated in computer and the approach of natural coordinates was adopted to build its equation of motion. In order to obtain appropriate natural coordinates, a two-step selection method was chosen, which based on concept of natural coordinate system (NCS). The two-step method treats selecting natural coordinates for a rigid element as building an actual NCS which should be adapted from a standard NCS. In order to automate the process of adaptation for 18 rigid elements in the model of Big Pendulum Hammer, a four-step self-adaptation method was also adopted, which can help automate the selection of natural coordinates for multi-rigidbody systems.

Abstract: A self-adaptation method for natural-coordinate systems is proposed, in order to automate the selection of natural coordinates for each rigid element of a multibody system. The four-step method includes: First, find out all empty positions, which come from the feature points or vectors of the joints attached to the element, and give equal weight to them; second, delete redundant empty positions and add their weight to the unique one; third, select at most four empty positions which have a maximum total weight and can be occupied by a natural-coordinate system at the same time; fourth, the standard natural-coordinate system on the element can adapt itself to the selected empty positions, leading to an actual natural-coordinate system, which contains twelve rational natural coordinates for the element. The implementation of the method has been achieved on a multibody dynamics and motion analysis platform, InteDyna, with the result that modeling efficiency is enhanced and model quality improved.

Abstract: Because of special structure and dynamic behavior, the dynamic equations of metamorphic mechanism are variable during the process of configuration change. In order to combine dynamics analysis and structure design of metamorphic mechanisms intimately, a new method of forming dynamic model of metamorphic mechanisms is proposed based on fully Cartesian coordinate’s method and the relation between origin mechanism and sub-configuration. A new concept named origin constraint equation is introduced which can be converted into constraint equations of each sub-configuration easily by adding corresponding constraint equations of configuration change. Constraint equations commonly used in configuration change and dynamic equations of each configuration are given in the form of natural coordinates. Finally, a four-bar spherical metamorphic mechanism is used as an example to validate this dynamic modeling method.