Gruebler's equation counts independent coordinates needed to define a mechanism position.
Gruebler's equation for planar mechanisms: F=3(n-1)-2j₁-j₂. F=1 is a constrained single-input mechanism. F=0 is a structure; F<0 is over-constrained. Spatial mechanisms use 6(n-1)-Σ constraints.
A four-bar linkage has n=4, j=4 so F=1.
Mobility counts tell you whether a mechanism will move as intended, so you can catch designs that are locked or have unwanted freedom.
Gruebler's equation counts independent coordinates needed to define a mechanism position.
Mobility counts tell you whether a mechanism will move as intended, so you can catch designs that are locked or have unwanted freedom.
The mobility of a planar mechanism, equal to three times the number of moving links minus two times the number of joints minus the higher-pair count.
The mechanism is a rigid structure, not a moving linkage, so it cannot move without deformation or a change in design.
Typical applications include checking that a proposed hinge design does not lock up when assembled, counting the degrees of freedom of a robot gripper and verifying that a linkage has a single input-output motion.
Study "Mechanisms and linkages" first (topic 83 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Links n, lower pairs j₁, higher pairs j₂. Redundant constraints. Degrees of freedom of robot arms.
A four-bar linkage has n=4, j=4 so F=1.
The next topic is "Cams and followers", which builds directly on this one.
It is classed as Advanced in Engineering Mechanics (topic 84 of 106). It is an advanced topic. It assumes you are comfortable with the intermediate topics in Engineering Mechanics.
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