# Assemblies

Components that aggregate several joints for analytic loop handling

# Package Contents

 JointUPS Universal - prismatic - spherical joint aggregation (no constraints, no potential states) JointUSR Universal - spherical - revolute joint aggregation (no constraints, no potential states) JointUSP Universal - spherical - prismatic joint aggregation (no constraints, no potential states) JointSSR Spherical - spherical - revolute joint aggregation with mass (no constraints, no potential states) JointSSP Spherical - spherical - prismatic joint aggregation with mass (no constraints, no potential states) JointRRR Planar revolute - revolute - revolute joint aggregation (no constraints, no potential states) JointRRP Planar revolute - revolute - prismatic joint aggregation (no constraints, no potential states)

# Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

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:

 P Prismatic joint R Revolute joint S Spherical joint U Universal joint

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

This package contains the following models:

#### Content

ModelDescription
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 compromise: 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.