8.1 Mechanisms
Consider a pair of adjustable vice grips.
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
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)
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.
Some basic mechanism types are listed below, and split into some suggested categories
8.1.1 Locking/Engaging
Snap-action mechanisms - typically bistable mechanisms, such as electrical breaker switches, or toggle mechanisms such as XXXX
Reversing Mechanisms - A mechanism that can disengage a transmission, and reverse direction of transmission
8.1.2 Motion Transmission/Transformation
8.1.3 Four Bar Linkages
Stop/Pause/Hesitation - a motion is produced that appears to come to a stop for a short period of time.
8.1.4 Reciprocating
8.1.5 Six Bar Linkages
These allow more complex motion, especially when ternary links are used.
In Watt linkages there are two ternary links touching,
In Stephenson linkages the terary links don't touch,
. Consider the equation, and the four basic kinematic inversions below. Keep in mind that the crank will be the shortest link, with length `s, and in all four cases will rotate continuously.