Kinematic Pairs (Joints) and Constraints

When we connect bodies (called links) together using joints, we introduce constraints, which reduce the total DOF of the system. Each joint allows certain motions and restricts others.

Common Joint Types and Their DOF

Joint Type

Symbol

Description & Motion Allowed

DOF (Spatial)

Constraints

Revolute

R

Hinge-like, allows only rotation about one axis.

1

5

Prismatic

P

Sliding, allows only linear motion along one axis.

1

5

Cylindrical

C

Allows rotation and translation about the same axis.

2

4

Spherical

S

Ball-and-socket, allows 3 rotational motions.

3

3

Screw

H

Coupled rotation and translation (like a nut on a bolt).

1

5

Planar

E

One surface sliding on another.

3

3