Version 1.0, August 31, 2001, Copyright, Hugh Jack 1993-2001

2. INTRODUCTION TO KINEMATICS OF MECHANISMS

 

· Consider a pair of adjustable vice grips.

 

 

·Some definitions,

  1. Machine - a collection of components that will do work.
  2. Mechanism - a collection of components to transform motion
  3. Kinematics - consider positions/velocities/accelerations in mechanical systems
  4. Structure - a collection of components to make larger static structures
  5. Statics - estimate forces in mechanisms that are in equilibrium
  6. Dynamics - determine motion that results when forces are out of balance
  7. Link - rigid body between joints
  8. Binary Link - has two joints only
  9. Ternary Link - has three joints
  10. Quaternary Link - has four joints
  11. Pair or Joint - a connection between two links
  12. Driver / Follower - the driver link will be driving the follower
  13. Kinematic Chain - a sequence of links making up a mechanism
  14. Open Loop - a snake like set of connected links
  15. Closed Loop - a kinematic chain has one or more links that go back in the chain
  16. Frame - a grounded or fixed link in a mechanism
  17. Spatial - in 3 dimensions
  18. 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

  1. Turning / Revolute - basically a pin joint (R)
  2. Prismatic - a slider (P)
  3. Screw/Helix - a nut and screw pair (H)
  4. Cylindric - a shaft in a collar (C)
  5. 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)

  1. - flat/planar - constrained to move over a plane
  2. - belt on pulley
  3. - meshing gears
  4. - sliding wheel on a surface
  5. - 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.

 

 

2.1 SOME POPULAR MECHANISMS

2.2 SKELETON DIAGRAMS FOR MECHANISMS

2.3 DOF AND THE KUTZBACH/GRUEBLER CRITERION

2.4 KINEMATIC/GEOMETRIC INVERSION

2.5 GRASHOF'S LAW

2.6 MECHANICAL ADVANTAGE

2.7 PRACTICE PROBLEMS

2.8 REFERENCES