Mechanisms & Mobility
From Mechanisms & Mobility
Mechanisms & Mobility
Learning goal
Classify links and kinematic pairs, count mobility with the Kutzbach/Gruebler equation, apply the Grashof criterion, and identify mechanism inversions.
Core ideas
A link is a rigid body carrying kinematic connections; a kinematic pair is the joint between two links. Lower pairs have surface contact (revolute R, prismatic P, cylindrical, spherical); higher pairs have line or point contact (cam-follower, gear teeth). A kinematic chain becomes a mechanism once one link is fixed as the frame; fixing a different link gives an inversion with the same relative motion but different absolute motion.
Mobility (degrees of freedom) of a planar mechanism follows the Kutzbach criterion: M = 3(N - 1) - 2 J1 - J2, where N is the number of links (including the frame), J1 the number of one-DOF lower pairs, and J2 the number of two-DOF higher pairs. M = 1 means a single input fully controls the motion.
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