Kinematic Pair

A connection between two parts that stay in contact while allowed to move relative to each other, like a hinge, a slider, or meshing gears.

A kinematic pair is a basic concept in mechanism design, introduced by the German engineer Franz Reuleaux, referring to a connection between two members that keeps them in contact while restricting their relative motion to a specific type. Kinematic pairs split into two classes by contact type. Lower pairs make surface contact and include the revolute pair (R, a hinge, 1 rotational degree of freedom), the prismatic pair (P, a slider, 1 translational degree of freedom), the screw pair, the cylindrical pair (2 degrees of freedom), and the spherical pair (3 degrees of freedom). Higher pairs make point or line contact, such as a cam and follower, meshing gear teeth, or a wheel rolling on the ground. What robotics calls a 'joint' is a kinematic pair: a revolute joint is a revolute pair, and a prismatic joint is a prismatic pair. Grübler's formula for counting a mechanism's degrees of freedom works by subtracting the constraints each kinematic pair introduces from the members' total degrees of freedom. The original paper introducing DH parameters was even titled 'A kinematic notation for lower-pair mechanisms based on matrices.'

ExampleA planar four-bar linkage: including the frame, it has 4 members and 4 revolute pairs; by the planar Grübler formula, degrees of freedom = 3×(4−1−4) + 4×1 = 1, so a single motor is enough to drive the whole mechanism.

Also called

Joint (Mechanism), Revolute Pair / Prismatic Pair, Lower Pair / Higher Pair

Related

Revolute Joint · Prismatic Joint · Spherical Joint · Degrees of Freedom (DoF) · Grübler's Formula · Four-Bar Linkage

Sources

Wikipedia: Kinematic pair
Lynch & Park, Modern Robotics（2017）2.2 节 Grübler 公式；参考文献 Denavit & Hartenberg 1955 (Chinese)