4569846498

Multibody systems simulation software 99
For any multibody systems model it is important that the analyst can determine
and understand the total degrees of freedom in the system. This can
be achieved by using the Gruebler equation:
Total DOF 6 (Number of parts 1) (Number of constraints) (3.44)
The parts count in (3.44) is reduced by one to account for the fact that the
non-moving ground is counted as a part in the system. The degrees of freedom
removed by typical constraint elements are summarized in Table 3.5
and may be used to complete the calculation.
At this stage it is necessary to introduce the subject of redundant constraints
and overconstraint checking. As a starting point consider a typical application
in a suspension that involves the modelling of the mounts attaching a control
arm or wishbone to the body or chassis. This is illustrated in Figure 3.19
Table 3.5
Degrees of freedom removed by constraint elements
Constraint element Translational Rotational Coupled Total
constraints constraints constraints constraints
Cylindrical joint 2 2 0 4
Fixed joint 3 3 0 6
Planar joint 1 2 0 3
Rack-and-pinion joint 0 0 1 1
Revolute joint 3 2 0 5
Spherical joint 3 0 0 3
Translational joint 2 3 0 5
Universal joint 3 1 0 4
Atpoint joint primitive 3 0 0 3
Inline joint primitive 2 0 0 2
Inplane joint primitive 1 0 0 1
Orientation joint primitive 0 3 0 3
Parallel joint primitive 0 2 0 2
Perpendicular joint primitive 0 1 0 1
Motion (translational) 1 0 0 1
Motion (rotational) 0 1 0 1
Coupler 0 0 1 1
BUSH
REAL
SYSTEM
BUSH
REVOLUTE JOINT
REVOLUTE JOINT
OVERCONSTRAINED
MODEL
Fig. 3.19
Redundant constraints in a suspension model