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### Modified Gruebler's Equation for Kinematics Calculator

Mechanics and Machine Design, Equations and Calculators

Modified Gruebler's Equation for Kinematics Calculator

For a planar mechanism, the degree of freedom (mobility) is given by Gruebler's Equation:

In kinematics the number of mobile links is:

Gruebler's Equation - degrees of freedom (mobility)

*F = 3(n – 1) – 2 f _{1} *

Modified Gruebler's Equation - degrees of freedom (mobility)

*F = 3(n – 1) – 2 f _{1} - 1 f_{2}*

where

*f _{1}* =
Total number of pin joints (some joints count as f = ½, 1, 2, or 3)

*f*= number of roll-slide contact joints

_{2}n = Total number of links (including a fixed or single ground link)

For example,

Example 1: Slider-crank n = 4, *f _{1}* = 4,

*F*= 1

Figure 1 - 4 links (including ground), 4 joints

Example 2: 4-Bar linkage n = 4, *f _{1}* = 4,

*F*= 1

Source:

- Erdman, Arthur G., George N. Sandor, and Sridhar Kota, Mechanism Design, Vol. 1, 4th ed.,

New York: Prentice Hall, Inc.: - MIT, Mechanical Design Contest Presentation

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