A link, is an (assumed) rigid body which possesses at least two nodes which are points for attachment to other links.

## Joints:

A joint is a connection between two or more links, which allows some motion, or potential motion, between the connected links. Depending upon the number of links at the joint, a joint can be binary, ternary or quaternary.

## Kinematic Pairs:

Kinematic pair is a joint of 2 links having relative motion between them. Kinematic pairs can be classified in several ways:

1. By the type of contact between the elements, line, point, or surface.

2. By the number of degrees of freedom allowed at the joint.

3. By the type of physical closure of the joint: either force or form closed.

By the type of contact between the elements, line, point, or surface:

a. Lower Pairs: A pair of links with surface or area contact between them. Examples includes: Nut turning on a screw, Shaft rotating in a bearing, etc.

b. Higher Pair: A pair of links with point or line contact between them. Examples includes: Wheel rolling on a surface (line contact), Tooth gears (line contact), Ball and roller bearing (point contact), Cam and follower pair (can be point or line contact), etc.

At a microscopic level, a block sliding on a flat surface actually has contact only at discrete points, which are the tops of the surfaces’ asperities. The main practical advantage of lower pairs over higher pairs is their better ability to trap lubricant between their enveloping surfaces. This is especially true for the rotating pin joint. The lubricant is more easily squeezed out of a higher pair, non-enveloping joint. As a result, the pin joint is preferred for low wear and long life, even over its lower pair cousin, the prismatic or slider joint.

By the number of degrees of freedom allowed at the joint or the nature of relative motion:

a. Revolute Pair: When one link has a turning or revolving motion relative to the other, they constitute a turning or revolving or revolute pair. This joint has 1 degree of freedom.

b. Prismatic or Sliding Pair: When 2 links have a sliding motion relative to each other, they form a prismatic or sliding pair. This joint has 1 DOF.

c. Rolling Pair: When the links of a pair have rolling motion relative to each other, they form a rolling pair. This joint has 1 degree of freedom. Example includes ball and roller bearings, wheel rolling on a surface, etc.

d. Cylinderic Pair: When 2 links have a sliding motion as well as turning or revolving motion relative to each other, they form a prismatic or sliding pair. This joint has 2 DOF.

e. Screw Pair (Helical Pair):  When the nature of contact between the elements of a pair is such that one element can turn about the other by screw threads, it is known as screw pair or helical pair. This joint has 1 DOF.

Motion of either the nut or the screw with respect to the other results in helical motion. If the helix angle is made zero, the nut rotates without advancing and it becomes the pin joint. If the helix angle is made 90 degrees, the nut will translate along the axis of the screw, and it becomes the slider joint.

f. Screw Pair (Helical Pair):  When the nature of contact between the elements of a pair is such that one element can turn about the other by screw threads, it is known as screw pair or helical pair. This joint has 1 DOF.

g. Spherical Pair: When one link in the form of a sphere turns inside a fixed link, it is a spherical pair. Example, Ball and socket joint. This joint has 3 DOF.

By the type of physical closure:

a. Form Closed: A form-closed joint or pair is kept together or closed by its geometry. Example: a pin in a hole or a slider in a two-sided slot are form closed.

b. Forced Closed: A force-closed joint, such as cam and follower, requires some external force to keep the elements of the pair together or closed. This force could be supplied by gravity, spring, or any external means. Other examples includes slider on a surface.

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