and OR , and are the minimum conditions for a mechanism

  • Converts linear motion of piston to rotational motion at crank (reciprocating engine) or vise versa (reciprocating compressor)
  • Rotational motion is more favorable to deal with due to its continuous nature Kinematic Diagram vs. Construction Drawing
  • A Mechanism is characterized by the number of pairs and number of links
  • Inversion of a Mechanism involves implementing changes in the mechanism (i.e. changing the fixed link) to get a different variation of the mechanism, without changing the number of links or pairs

  • Converts rotational motion to oscillatory motion
  • Achieves quick-return behavior

This is not the only mechanism to achieve the quick return behavior, but thatโ€™s what it is famous for

This inversion of the Slider-crank mechanism is called Crank-shaper mechanism

Extreme positions are tangent to the circle of the connecting rod (which behaves as a crank)


  • The oscillation of the cylinder, which has large inertial, causes unbalance and dynamic forces, thus its usage has declined

01:24:53 Usually the number of inversions in a mechanism equals the number of links, but some inversions are not logical and are not considered (e.g. fixing piston in Slider-crank mechanism)


  • Achieves ellipse equation by relating , and using the fact that

This mechanism is a great example of how mechanisms are used for satisfying mathematical equations (which is then applied in mechanical computers)

  • Any mechanism is characterized by inputs and outputs in terms of mathematical relations

There are three Types of motion

Pay attention to the relation between Kinematic diagram and Construction drawing

Fixing link A will not give a new inversion because it will be the same as fixing B only giving vertically reciprocating Scotch yoke mechanism


  • Rotation at A โ†’ Rotation of Frame โ†’ Rotation at B โ‡’ Coupling of shafts with parallel, shifted axes
  • There is a shift between axis of rotation of A and axis of rotation of B
  • Base is link AB

Maintaining 90 degree angle

  • To maintain 90 degree between A and B, the frameโ€™s center need to rotate about a point that lies at the center between AB