4569846498

Multibody systems simulation software 95
Table 3.1
Basic constraint element equations
Constraint Full equation Abbreviated form
Atpoint { a } 1 ({R i } 1 {r I } 1 ) ({R j } 1 {r J } 1 ) {d IJ } 1
Inplane d [({R i } 1 {r I } 1 ) ({R j } 1 {r J } 1 )] • {a J } 1 {d IJ } 1 • {a J } 1
Perpendicular p {a I } 1 • {a J } 1 {a I } 1 • {a J } 1
Angular arctan ({x i } 1 • {y j } 1 /{x i } 1 • {x j } 1 ) IJ
Table 3.2
Force contributions for basic constraint elements
Constraint Part i force Part j force
Atpoint {} {}
Inplane [A 1j ]{a J } j d [A 1j ]{a J } j d
Perpendicular 0 0
Angular 0 0
Table 3.3
Moment contributions for basic constraint elements
Constraint Part i moment Part j moment
Atpoint [B i ] T {r I } i [A i1 ] [B j ] T {r J } i [A j1 ]
Inplane [B i ] T {r I } i [A ij ]{a J } j d [B j ] T {a J } j [A j1 ]({R i } 1 [A 1i ]{r I } i {R j } 1 ) d
Perpendicular [B i ] T {a I } i [A ij ]{a J } j p [B j ] T {a J } j [A ji ]{a I } i p
Angular [B i ] T {z i } i [B j ] T {z j } j
In applying this constraint it is assumed that other system constraints will
maintain the z-axes of the two parts to remain parallel as shown in Figure 3.16.
The moment acting on part i is given by {z i } 1 and on part j by {z j } 1 .
Transforming into the Euler axis system for each part gives a moment in
the co-ordinate system for part i equal to [B i ] T {z i } i and on part j by
[B j ] T {z j } j .
The equations associated with each of the four basic constraint elements
are summarized in Table 3.1.
The force and moment contributions to each part in the generalized
co-ordinates are summarized in Table 3.2 and Table 3.3.
3.2.7 Standard joints
As stated there are a number of mechanical type joints that may be used to
constrain the motion of bodies. Examples of some of the most commonly
used joints are shown in Figure 3.17.
Of the joints shown in Figure 3.17 the spherical, revolute, translational,
cylindrical and universal will figure most prominently in this text, particularly
with regard to the modelling of suspension systems. The concept of an
I marker on one part connecting to a J marker on another part is used again
for joint elements. An example of the syntax used to define a joint in
MSC.ADAMS is shown below:
JOINT/02,I0602,J0902,SPH