A new finite element to represent prismatic joint constraints in mechanisms

Among existing kinematic analysis methods of mechanisms, the techniques based on finite elements represent a generally applicable alternative which enable a wide variety of problems to be solved, including linear (velocities, accelerations, jerk, …) and non-linear ones (position). To modelize a mechanism via these techniques, the link element may be used to introduce a distance constraint between two points. The stiffness matrix assembly of these link elements enables stiffness matrix construction from the model, from which the kinematic behaviour of the mechanism may be extracted.Normally kinematic link conditions introduced directly into the system stiffness matrix are used to introduce point to line constraints like those originated by prismatic joints. A new finite element is presented in this paper, defined by its stiffness or geometric matrix, capable of alternatively modelizing the constraints imposed by the prismatic joint. This new element offers numerous advantages against the procedure based on anterior link conditions, particularly in the case of non-linear problems.