Lecture 12 The Power of Kinematic Inversion: One Kinematic Chain, Many Mechanisms

Principle of Kinematic Inversion

Kinematic Inversion : The process of fixing different links of the same Kinematic Chain to produce distinct mechanisms is called Kinematic Inversion.

The relative motions between various links remains unchanged under Kinematic Inversion.

[ Source: Theory of Mechanisms and Machines - A Ghosh and Mallik A K - Affiliated East - West Press ]

Inversions of Four bar linkage / (planar) mechanism (4R Mechanism):

In four bar linkage / ( planer) mechanism, lengthwise Crank is the shortest link and Frame is the longest link. Coupler and Follower link lengths are intermediate.

1st Inversion : Crank - Rocker Mechanism :

Shorter (left side) link with respect to frame [Crank - Link 2] revolves and the comparatively longer (right side) link with respect to frame [Follower - Link 4] rocks (oscillates).

Crank-Rocker Mechanism

2nd Inversion : Double Crank Mechanism OR Drag - link Mechanism :

Shortest link [Crank - Originally second link ] is Frame [ Revised 1st Link].

Second link = Driving Crank = Originally [ link 3 - coupler ]

Third link = Coupler = Originally [link 4 - follower]

Fourth link = Driven Crank = Originally [link 1 -frame]

Originally coupler [link - 3] and frame [ link - 1] are side links in Double Crank Mechanism that revolves.

Example of special case of Double Crank Mechanism is Coupling Rod of Locomotive wherein both Driving Crank and Driven Crank are of equal length in terms of dimensions.

3rd Inversion : Double Rocker Mechanism

Motion-transfer link [Coupler-Originally third link] is Frame [Revised 1st link].

Second link = Driving Rocker = Originally [link 4 - follower]

Third link = Coupler = Originally [link 1 - Frame]

Fourth link = Driven Rocker = Originally [link 2 - crank]

Originally follower [link - 4] and crank [link - 2] are side links in Double Rocker Mechanism that rock (oscillate).

Note : Driving Rocker [Originally link 4 - follower] is NOT the shortest link.

4th Inversion : Rocker - Crank Mechanism

Follower link [Originally Comparatively longer (Right) side link] is Frame [Revised 1st Link]

Second link = Driving Rocker = Originally [link 1 - frame]

Third link = Coupler = Originally shortest (left) side link [link - 2 crank ]

Fourth link = Driven Crank = Originally [link - 3 coupler ]

Note :

Full rotation of Originally 'Coupler link' [link - 3] as crank in 4th inversion of Four bar linkage / (planer) mechanism is observed even though, revised Driven crank [Originally 'Coupler link' ( link - 3)] is not the shortest link.

Study Guide for Kinematics of Machines

Quiz: Short Answer Questions

Instructions: Answer the following question in 2-3 sentences, based on the provided source material.

9. Explain the principle of kinematic inversion.

--------------------------------------------------------------------------------

Answer Key

9. Kinematic inversion is the process of producing distinct mechanisms by fixing different links of the same kinematic chain. The most important aspect of this principle is that the relative motions between the various links remain unchanged, regardless of which link is fixed.