## 8.1 Mechanisms

• 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.

• 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

Clamping Mechanisms - vices, collets, etc.

Locational Devices - self alining/centering devices

Ratchets and Escapements - A locking mechanism, like a ratchet wrench or winch

Indexing Mechanisms - e.g. the geneva mechanism

Reversing Mechanisms - A mechanism that can disengage a transmission, and reverse direction of transmission

### 8.1.2 Motion Transmission/Transformation

Linear Actuators - produce a straight line motion. can be done with threads, or hydraulic cylinders

Fine Adjustments - screws, wedges, etc. - these can overcome imperfections during manufacture

Couplings and Connectors - transmit rotations between rotating shafts. e.g. pulleys and belts

Sliding Connectors - transmit linear motions in different directions

Swinging or Rocking Mechanism - produce cyclic motions

Stop/Pause/Hesitation - a motion is produced that appears to come to a stop for a short period of time.

Curve Generators - mechanisms set up to follow complex paths - typically four bar linkages.

Straight Line - mechanisms are set up to generate straight line motions

### 8.1.4 Reciprocating

Reciprocating Mechanisms - converts a rotational motion to a linear motion

• These allow more complex motion, especially when ternary links are used.

•. 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.