Assemblies

The joints in this package are mainly designed to be used in kinematic loop structures. Every component consists of 3 elementary joints. These joints are combined in such a way that the kinematics of the 3 joints between frame_a and frame_b are computed from the movement of frame_a and frame_b, i.e., there are no constraints between frame_a and frame_b. This requires to solve a non-linear system of equations which is performed analytically (i.e., when a mathematical solution exists, it is computed efficiently and reliably). A detailed description how to use these joints is provided in MultiBody.UsersGuide.Tutorial.LoopStructures.AnalyticLoopHandling.

The assembly joints in this package are named JointXYZ where XYZ are the first letters of the elementary joints used in the component, in particular:

For example, JointUSR is an assembly joint consisting of a universal, a spherical and a revolute joint.

This package contains the following models:

Content

Model	Description
JointUPS	Universal - prismatic - spherical joint aggregation
JointUSR	Universal - spherical - revolute joint aggregation
JointUSP	Universal - spherical - prismatic joint aggregation
JointSSR	Spherical - spherical - revolute joint aggregation with an optional mass point at the rod connecting the two spherical joints
JointSSP	Spherical - spherical - prismatic joint aggregation with an optional mass point at the rod connecting the two spherical joints
JointRRR	Revolute - revolute - revolute joint aggregation for planar loops
JointRRP	Revolute - revolute - prismatic joint aggregation for planar loops

Note, no component of this package has potential states, since the components are designed in such a way that the generalized coordinates of the used elementary joints are computed from the frame_a and frame_b coordinates. Still, it is possible to use the components in a tree structure. In this case states are selected from bodies that are connected to the frame_a or frame_b side of the component. In most cases this gives a less efficient solution, as if elementary joints of package Modelica.Mechanics.MultiBody.Joints would be used directly.

The analytic handling of kinematic loops by using joint aggregations with 6 degrees of freedom as provided in this package, is a new methodology. It is based on a more general method for solving non-linear equations of kinematic loops developed by Woernle and Hiller. An automatic application of this more general method is difficult, and a manual application is only suited for specialists in this field. The method introduced here is a compromize: It can be quite easily applied by an end user, but for a smaller class of kinematic loops. The method of the "characteristic pair of joints" from Woernle and Hiller is described in:

Woernle C.:

Ein systematisches Verfahren zur Aufstellung der geometrischen Schliessbedingungen in kinematischen Schleifen mit Anwendung bei der Rückwärtstransformation für Industrieroboter.
Fortschritt-Berichte VDI, Reihe 18, Nr. 59, Duesseldorf: VDI-Verlag 1988, ISBN 3-18-145918-6.
 

Hiller M., and Woernle C.:

A Systematic Approach for Solving the Inverse Kinematic Problem of Robot Manipulators.
Proceedings 7th World Congress Th. Mach. Mech., Sevilla 1987.