Mechanisms — degrees of freedom

Recent Blogs

Planar Pair diagram
Planar Pair: Exact Three-Coordinate Pose Geometry
Planar Pair explained — the plane-on-plane kinematic pair gives 3 DOF in machine-tool slides, surface grinders, and flatbed printers. Formula, examples, tradeoffs.
Twelve-bar Linkage diagram
Twelve-bar Linkage: Planar Mobility Count Calculator
Calculate the planar lower-pair mobility count from link and joint totals. Connection geometry and constraint independence must be checked separately for a real linkage.
Three-link Kinematic Chain diagram
Three-link Kinematic Chain: Generic Planar Mobility
Compare open and closed ideal three-link chains, counting ground as one link. Calculate nominal mobility and joint constraints without solving dimensions or motion.
Ten-bar Linkage diagram
Ten-bar Linkage: Nominal Planar Mobility Calculator
Explore a conceptual ten-link chain and calculate its nominal planar mobility from link and revolute-joint counts. Dimensions and motion paths are not solved.
Eight-bar Linkage diagram
Eight-bar Linkage Mechanism Explained: How It Works, Parts, Diagram and Grübler DOF Formula
Explore a Jansen-type eight-bar walking leg with a calculated foot path. Adjust scale, crank radius and speed; see rigid links, joint count, travel and gait...
Mechanism (engineering) diagram
Planar Mechanism Mobility: Constraint-Count Worksheet
Calculate the generic planar mobility count from links and joints, and explore a four-bar example. Constraint independence and actual geometry require separate checks.
Mechanical Translation diagram
Lead-Screw Mechanical Translation Calculator
Explore a guided lead-screw drive and calculate ideal turns, travel, speed and torque-derived thrust using entered lead, speed, run time and efficiency.
Kinematic Chain diagram
Kinematic Chain: Four-Bar Animation and Mobility Count | FIRGELLI
Explore a fixed four-bar linkage and calculate the planar lower-pair count 3(n−1)−2j. Link and joint totals do not specify geometry or establish constraint independence.