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96 Mutibody Systems Approach to Vehicle Dynamics
Revolute Spherical Cylindrical Translational
Planar
Fixed Universal Rack & Pinion
Fig. 3.17 Examples of commonly used joint constraints. (This material
has been reproduced from the Proceedings of the Institution of Mechanical
Engineers, K2 Vol. 213 ‘The modelling and simulation of vehicle handling.
Part 1: analysis methods’, M.V. Blundell, page 108, by permission of the Council
of the Institution of Mechanical Engineers)
Table 3.4
Joint constraints in MSC.ADAMS
Joint type Constraints Abbreviated equation
Trans’ Rot’ Total
Spherical 3 0 3 {d IJ } 1 0
Planar 1 2 3 {z I } i • {x J } j 0, {z I } i • {y J } j 0, {d IJ } 1 • {z J } j 0
Universal 3 1 4 {d IJ } 1 0, {z I } i • {z J } j 0
Cylindrical 2 2 4 {z I } i • {x J } j 0, {z I } i • {y J } j 0, {d IJ } 1 • {x J } j 0,
{d IJ } 1 • {y J } j 0
Revolute 3 2 5 {d IJ } 1 0, {z I } i • {x J } j 0, {z I } i • {y J } j 0
For a spherical joint the I marker and J marker are defined to be coincident
at the centre of the joint but the orientation of the markers is irrelevant. For
other joints such as the revolute, cylindrical and translational it is necessary
not only to position the joint through the co-ordinates of the I and J marker
but also to define the orientation of the axis associated with the mechanical
characteristics, rotation and/or translation, of the joint. The method used in
MSC.ADAMS is to use the local z-axis of the markers to define the axis,
the most convenient method of doing this often being to define a ZP parameter
for each marker. For the universal joint the axes of the spindles need to
be defined perpendicular to one another. For this joint the I and J marker
are defined to be coincident with the z-axis of each orientated to suit the
axis of the spindle on the side of the joint associated with the body to which
the marker belongs.
The vector equations that have been derived earlier for the basic constraints
can be applied in a similar manner to generate constraint equations for the
standard joints. A spherical joint, for example, fulfils exactly the same function
as an atpoint joint primitive. Examples of constraint equations for some
commonly used joints are shown in Table 3.4.