Kinematic pair facts for kids

In classical mechanics, a kinematic pair is like a special connection between two physical objects. This connection makes sure the objects can only move in certain ways relative to each other. Think of it as a rulebook for how two parts of a machine can move together. A German engineer named Franz Reuleaux came up with this idea to better understand how machines work.

What is a Kinematic Pair?

Kinematics is a part of classical mechanics that studies how things move. It looks at the motion of points, objects, and groups of objects without worrying about what causes the motion. You can think of kinematics as the "geometry of motion." For more details, see Kinematics.

When two objects are connected to form a kinematic pair, they are often called 'rigid bodies'. In machines, robots, or other mechanical systems, these two objects are usually called 'links'.

There are two main types of kinematic pairs: higher pairs and lower pairs.

How Kinematic Pairs Work

Imagine connecting two strong, unbending objects. Reuleaux explained that these connections fall into two groups:

• Higher pairs: In these connections, the two parts touch at just one point or along a single line. An example is a ball bearing or a cam and its follower. The way points on each object move can be very different.
• Lower pairs: Here, the two parts touch over a larger area, like a surface. Examples include a pin connection (like a hinge), a crosshead, or a ball and socket joint. With lower pairs, points on both objects move in similar ways. If you swapped which part was fixed, the motion wouldn't change.

Lower Pairs: Surface Contact

A lower pair is a perfect joint where one surface of a moving object stays in contact with a matching surface on a fixed object. This means there's a large area of contact between the two parts. Examples include a nut and a screw, or a universal joint connecting two shafts.

Here are some common types of lower joints:

Revolute Joint (Hinge)

A revolute R joint is like a simple hinge. It makes sure a line in the moving part stays lined up with a line in the fixed part. Also, a flat surface on the moving part, which is at a right angle to this line, stays in contact with a similar flat surface on the fixed part. This type of joint allows movement in only one way: rotation. It has one degree of freedom.

Prismatic Joint (Slider)

A prismatic P joint is a slider. It makes sure a line in the moving part stays lined up with a line in the fixed part. A flat surface on the moving part, parallel to this line, stays in contact with a similar parallel surface on the fixed part. This joint allows movement in only one way: sliding back and forth. It also has one degree of freedom.

Screw Joint (Helical)

A screw H joint has threads cut into two parts, like a screw and a nut. When you turn one part, it also slides along the other. This joint combines turning and sliding motion. It has one degree of freedom.

Cylindrical Joint

A cylindrical C joint makes sure a line in the moving part stays lined up with a line in the fixed part. It's like having both a revolute (turning) and a prismatic (sliding) joint combined. This joint allows movement in two ways: rotation and sliding. It has two degrees of freedom.

Universal Joint

A universal U joint connects two rigid parts whose axes are angled to each other. It's made of two revolute joints that cross each other at right angles.

Spherical Joint (Ball and Socket)

A spherical S joint is also known as a ball and socket joint. It requires a point in the moving part to stay in the same place relative to the fixed part. This joint allows movement in three ways: rotation around three different axes. It has three degrees of freedom.

Planar Joint

A planar joint makes sure a flat surface in the moving part stays in contact with a flat surface in the fixed part. This joint allows movement in three ways: it can slide in two directions along the fixed surface, and it can rotate around an axis that's straight up from the fixed surface. It has three degrees of freedom.

Parallelogram Joint

A parallelogram Pa joint is made of four links connected by four revolute joints. These joints are arranged at the corners of a parallelogram shape.

Higher Pairs: Point or Line Contact

A higher pair is a connection where a curve or surface on the moving part touches a curve or surface on the fixed part. This contact happens at a single point or along a line. For example, the contact between a cam and its follower is a higher pair, called a cam joint. Similarly, the teeth of two gears meshing together are also cam joints. A wheel rolling on a surface is another example.

Wrapping Pairs: Multiple Point Contact

A wrapping pair is very similar to a higher pair. It involves things like belts and chains. A belt driving a pulley is a good example. While higher pairs have point or line contact, wrapping pairs have contact at multiple points along the belt or chain.

Understanding Joint Notation

Why We Use Joint Notation

Machines, robots, and manipulators are usually built from 'links' (the rigid parts) connected by 'joints'. For example, a SCARA robot connects a moving platform (called the 'end effector') to its base using a single chain of links and joints. Parallel manipulators, like the Gough-Stewart mechanism, connect the moving platform to the base using several chains of links. These chains are called 'limbs' or 'legs'.

'Topology' describes how the links and joints are arranged to form a robot or mechanism. Joint notation is a handy way to describe this arrangement.

Common Joint Abbreviations

Joints are given short names:

• Prismatic: P
• Revolute: R
• Universal: U
• Cylindrical: C
• Spherical: S
• Parallelogram: Pa

If a joint is 'actuated' (meaning it's actively controlled, like by a motor), it's shown with an underline: P, R, U, C, S, Pa.

How to Read Joint Notation

Joint notation tells you the type and order of joints in a mechanism. It lists the joints starting from the base of the machine all the way to the moving platform.

For example, the notation for a SCARA robot is RRP. This means it has two active revolute joints (RR) followed by one active prismatic joint (P). If joints are repeated, you can use a number. So, the SCARA robot could also be written as 2RP.

For parallel mechanisms, like the Gough-Stewart mechanism, the notation is 6-UPS or 6(UPS). This means it has six identical serial limbs. Each limb is made of a universal U joint, an active prismatic P joint, and a spherical S joint. Parentheses () are used to group the joints within each individual limb.

See also

In Spanish: Par cinemático para niños

• Mechanism (engineering)
• Manipulator (device)
• Linkage (mechanical)