Mobility of Planar Mechanisms – Degrees of Freedom using Kutzbach Criterion

4 example problems demonstrate how to calculate mobility of planar mechanisms, which is their Degrees of Freedom (DOF), using the Mobility Equation, also called the Kutzbach Criterion.

The toughest part is determining whether each joint is a J1 Lower Pair (like sliders) which allow 1 degree of freedom and a J2 Higher Pair or Upper Pair (like pin joints) that allow 2 degrees of freedom.

Gruebler’s Equation is almost the same form as the Kutzbach Criterion, except that the Kutzbach Criterion considers all ground connections to be a single fixed link, whereas Gruebler’s Equation allows for multiple separate ground links, and subtracts each one individually. I only use the Kutzbach Criterion in this video since it’s more intuitive to most students to just ignore all ground connections.

This topic is often the first one covered in Design of Machinery or Machines and Mechanisms college courses, which are usually junior or senior level Mechanical Engineering courses. Some of the more popular textbooks covering this topic are Theory of Machines and Mechanisms by Pennock, and Design of Machinery by Norton.


TIMECODES

0:00 Kutzbach Criterion – Mobility Equation
2:09 Difference between J1 Lower Pair and J2 Upper Pair
5:20 What if Mobility = -1, 0, or 2?
7:08 How to analyze non-obvious joint types
10:34 How to Check Your Final Answer