2. INTRODUCTION TO KINEMATICS OF MECHANISMS

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Consider a pair of adjustable vice grips.

Some definitions,

Machine - a collection of components that will do work.

Mechanism - a collection of components to transform motion

Kinematics - consider positions/velocities/accelerations in mechanical systems

Structure - a collection of components to make larger static structures

Statics - estimate forces in mechanisms that are in equilibrium

Dynamics - determine motion that results when forces are out of balance

Link - rigid body between joints

Binary Link - has two joints only

Ternary Link - has three joints

Quaternary Link - has four joints

Pair or Joint - a connection between two links

Driver / Follower - the driver link will be driving the follower

Kinematic Chain - a sequence of links making up a mechanism

Open Loop - a snake like set of connected links

Closed Loop - a kinematic chain has one or more links that go back in the chain

Frame - a grounded or fixed link in a mechanism

Spatial - in 3 dimensions

Relative/Absolute - a position, velocity, etc. is measured based on a fixed (absolute) or moving (relative) point.

A Degree Of Freedom (DOF) is an independently controllable variable. As an example, a machine that has two degrees of freedom might need two motors to control it.

Lower Pairs, - constrained position/orientation of both sides of the joints are identical

Turning / Revolute - basically a pin joint (R)

Prismatic - a slider (P)

Screw/Helix - a nut and screw pair (H)

Cylindric - a shaft in a collar (C)

Globular/Spherical - a ball joint (S)

Higher pairs include, - typically other equations are needed to constrain the joints, such as gear ratios (if the joint has more than a single degree of freedom)

- flat/planar - constrained to move over a plane

- belt on pulley

- meshing gears

- sliding wheel on a surface

- etc.

The definition of higher/lower pairs given in Shigley [1995] is, "the lower pairs, such as the pin joint, have surface contact between the pair elements, while higher pairs, such at the connection between a cam and its follower, have line or point contact between the surface elements." They go on to point out that the definition is not exact, which is somewhat disappointing.

A better definition of a higher pair is - A higher pair is not a lower pair, where a lower pair permits the following relative motions between links; circular, linear, helical, cylindrical, spherical, planar.

If a link has one joint, it is a unary link. A link with two joints is binary, with three it is ternary, with four it is quaternary, etc.

Planar linkages use lower order pairs, and are constrained to a single plane of motion.