# Wedge Constraint

Conditions for the application of wedge constraint are as follows:

- There is a regular contact between two objects.
- Objects are rigid.

The relative velocity perpendicular to the contact plane of the two rigid objects is always zero if there is a regular contact between the objects. Wedge constraint is applied for each contact. In other words, components of velocity along the perpendicular direction to the contact plane of two objects is always equal if there are no deformations and they remain in contact (Fig. 5).

**Fig. 5**

**If a rod moves vertically downward on the surface of movable wedge of mass as shown in Fig. 6, the relation between the velocity of rod and that of the wedge at any instant can be found using the concept above.**

*Note:*

Fig. 6

Fig. 6

Using wedge constraint, component of the velocity of rod along perpendicular direction to the inclined surface is equal to the velocity of wedge along that direction.

i.e.,

*u*cos*Î¸*=*v*sin*Î¸**u*/

*v*= tan

*Î¸*

*u*=

*v*tan

*Î¸*