FLEXIBLE MECHANISMS THROUGH NATURAL COORDINATES AND COMPONENT SYNTHESIS - AN APPROACH FULLY COMPATIBLE WITH THE RIGID CASE

In this paper, a new method for the dynamic simulation of mechanisms w ith flexible bodies is presented. The principal object of this work is to define the flexible bodies based on the modelization technique dev eloped for rigid bodies using 'natural co-ordinates'. In the rigid cas e, each body is defined by means of the Cartesian co-ordinates of some of its points and the Cartesian components of some of its unit vector s, which are pointed in the direction of the pairs axis that connect t he body to its neighbours. In the flexible case, more variables are ne eded to define each body: on the one hand, two additional unit vectors are considered, rigidly attached to an already existing one, constitu ting a rigid orthogonal triedron, that will become the local reference frame of the body and on the other, amplitudes of static and dynamic modes, corresponding to component synthesis with fixed boundaries, are considered. There are an infinite number of dynamic modes, so that th e analyst should make a selection of the most relevant ones for each p roblem; their amplitudes will be added to the body variables. However, there are a finite number of static modes: three for each point, exce pt for the local frame origin, and two for each unit vector, except fo r the three that define the local frame; static modes amplitudes will not increase the number of body variables, since they may be expressed as the difference between the values of the points in local co-ordina tes (respectively, the values of the unit vectors) in a body deformed configuration and their values in the undeformed one, that is, they ma y be expressed in terms of the co-ordinates of points and components o f unit vectors that already define the body. This idea leads to a tota lly new dynamic formulation.