Configuration Space for Four-Bar Linkage

separation (

L

4

)

0.75

link lengths (

L

1

,

L

2

,

L

3

)

{1.35,2}

A planar four-bar linkage has four joints, so its configuration is described by four numbers. However, because the linkage is a closed chain, the resulting constraints make most configurations unattainable. The linkage's configuration space is a one-dimensional curve embedded in a four-dimensional space. The plot at left projects the configuration space onto the joint angles

(θ,ϕ)

of the first and third links. You can drag the locator to explore the set of reachable configurations. Because

θ

and

ϕ

are angles, this configuration space wraps around from

-π

to

π

. If any link is greater than the sum of the other three links, no valid configurations exist.