Mechanisms, Mobility & Motion Conversion

A mechanism constrains relative motion so an input produces a useful output. MIT’s design courses pair mechanism analysis with fabrication and testing because a mathematically mobile linkage can still bind from tolerance, deflect under load, or pass through a dangerous singular position ¹.

Specify motion before hardware

Write the need as a relationship:

Convert continuous 120 rpm rotary input into a 75 mm dwell-rise-dwell-return output, carrying 180 N, within 250 mm, for two million cycles.

Now compare cam, crank-slider, pneumatic cylinder, servo screw, or indexed belt. Required path, dwell, reversibility, backlash, force profile, speed, shock, lubrication, guarding, and maintenance decide.

Mobility and constraints

For a planar linkage with \(n\) links including ground, \(j_1\) one-degree joints, and \(j_2\) two-degree joints, the Kutzbach criterion is

It is a screening tool, not proof of useful motion. Geometry can create redundant constraints or special configurations. A four-bar has four links and four revolute joints, yielding \(M=1\): one input generally determines configuration.

Transmission angle and singularity

Near a toggle position, small input motion can produce very small output motion and high ideal force amplification. That can be useful for clamping, but forces and sensitivity rise while direction can become ambiguous. Identify singular and near-singular positions across the full tolerance range.

Design notebook exercise

For a package diverter, sketch three concepts: rotary flap, slider-crank pusher, and belt transfer. For each, draw the kinematic skeleton, count mobility, identify hard stops and pinch points, estimate peak force, and name the feature most sensitive to tolerance. Select only after making the comparison visible.