Degrees of Freedom (Grübler)
Compute the degrees of freedom (mobility) of a planar mechanism by the Grübler-Kutzbach equation, DOF = 3·(n − 1) − 2·j1 − j2, where n is the number of links (including the fixed one), j1 the 1-DOF joints (pin, slider) and j2 the 2-DOF joints. A four-bar linkage (n=4, j1=4) has DOF=1: a single input motion controls the whole mechanism. The basis of mechanism and robot synthesis. Enter the number of links, 1-DOF joints and 2-DOF joints.
Result
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Degrees of freedom (Grübler)
How many motors does it take to control a mechanism? The answer is the number of degrees of freedom (mobility), given by the Grübler-Kutzbach equation for planar mechanisms: DOF = 3·(n − 1) − 2·j1 − j2. Every free link in the plane has 3 degrees (x, y, rotation); the fixed link supplies the reference frame and drops out (n−1); each 1-degree joint (pin or slider) removes 2 degrees, and each 2-degree joint removes 1. The celebrated four-bar linkage (n=4, j1=4) gives DOF=1: a single input motor commands the entire motion. DOF=0 describes a rigid structure (a truss); a negative DOF, a statically indeterminate structure. It is the first calculation in the synthesis of any mechanism or robot. Enter the number of links and of joints.
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