Minimum number of links in a single degree-of-freedom planar mechanism

A planar mechanism is a mechanical system consisting of rigid bodies (links) connected by joints to form a closed chain or an open chain. A single degree-of-freedom planar mechanism is a mechanism that has only one independent motion or degree of freedom (DOF) in the plane of motion.

Higher and lower kinematic pairs

A kinematic pair is a connection between two links that allows relative motion between them. There are two types of kinematic pairs: higher pair and lower pair.

- A higher pair is a connection between two links that have line or surface contact. Examples: cam and follower, gear and rack, ball and socket joint.
- A lower pair is a connection between two links that have point contact. Examples: pin joint, slider joint, universal joint.

Minimum number of links

The minimum number of links in a single degree-of-freedom planar mechanism with both higher and lower kinematic pairs is four.

Explanation:

- A single degree-of-freedom planar mechanism has only one independent motion or DOF in the plane of motion. This means that it can only move in one direction or rotate around one axis.
- A mechanism with both higher and lower kinematic pairs requires at least one link with a higher pair and one link with a lower pair.
- To connect these two links, we need two additional links with lower pairs.
- Therefore, the minimum number of links in a single degree-of-freedom planar mechanism with both higher and lower kinematic pairs is four.

Example:

One example of a single degree-of-freedom planar mechanism with both higher and lower kinematic pairs is a four-bar mechanism. It consists of four links connected by four pin joints. One of the links has a cam and follower pair, and the other three links have slider joints. This mechanism can only rotate around one axis, and the motion is controlled by the cam and follower pair.