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Mechanism Design Explorer Lab

Explore how four-bar linkages, crank-slider mechanisms, and cam-follower systems convert rotary input motion into useful output. Compute degrees of freedom, classify linkages with Grashof's criterion, trace coupler curves, and analyze transmission angles for practical mechanism design.

Guided Experiment: Grashof's Criterion and Linkage Classification

How do the relative lengths of the four links determine whether a link can make a full rotation? What role does the shortest link play in classifying the mechanism?

Write your hypothesis in the Lab Report panel, then click Next.

Linkage Diagram

abcO₂O₄ABθ₂=45°μ=63.3°

Controls

Link Lengths
0°90°180°270°360°

Four-Bar Linkage Analysis

Degrees of Freedom (Gruebler)
M=3(n−1)−2j1−j2=3(4−1)−2(4)−0=1M = 3(n-1) - 2j_1 - j_2 = 3(4-1) - 2(4) - 0 = 1
Grashof Classification
Crank-Rocker
s+l≤p+q✓s + l \leq p + q \quad \checkmark
Output Angle
231.43°
Transmission Angle
63.3°
Coupler Point
(2.46, -0.86)
Mech. Advantage
1.9

Data Table

(0 rows)
#MechanismInput Angle (°)Output Angle (°)Trans. Angle (°)DOFGrashof Type
0 / 500
0 / 500
0 / 500

Reference Guide

Degrees of Freedom

Gruebler's equation determines the mobility of a planar mechanism. A mechanism with DOF = 1 needs exactly one input to define all positions.

M=3(n−1)−2j1−j2M = 3(n - 1) - 2j_1 - j_2

Here n is the number of links, j₁ is the number of full joints (revolute or prismatic), and j₂ is the number of half joints. A four-bar linkage has n = 4, j₁ = 4, giving M = 1.

Four-Bar Linkage

The four-bar linkage is the simplest closed-loop mechanism. It has four rigid links connected by four revolute joints, with the ground link fixed.

Links: a (crank),  b (coupler),  c (rocker),  d (ground)\text{Links: } a \text{ (crank)}, \; b \text{ (coupler)}, \; c \text{ (rocker)}, \; d \text{ (ground)}

Position analysis uses the law of cosines on the closure equation to find the output angle from a given input (crank) angle. The coupler point traces a curve called the coupler curve.

Crank-Slider Mechanism

A crank-slider converts rotary motion to linear (or vice versa). The crank drives a connecting rod attached to a slider constrained to move along a straight line.

x=rcos⁡θ+Lcos⁡ϕ,sin⁡ϕ=rLsin⁡θx = r\cos\theta + L\cos\phi, \quad \sin\phi = \frac{r}{L}\sin\theta

The piston displacement is nearly sinusoidal when L is much larger than r. The ratio L/r controls how symmetric the forward and return strokes are.

Grashof's Criterion

Grashof's criterion determines whether the shortest link in a four-bar mechanism can make a full revolution relative to the other links.

s+l≤p+qs + l \leq p + q

Where s is the shortest link, l is the longest, and p, q are the remaining two. If satisfied and the shortest link is the crank, you get a crank-rocker. If the shortest is the ground, a double-crank. The transmission angle μ indicates force transfer quality and should stay between 40° and 140°.