The muscles in animals are complex structures consisting bundles of long fibers that contract in response to chemical signals. When contractile fibers are lengthened and when they are bundled, how the resulting pull changes depends on the physics of how connected springs add their forces. In order to understand how this works, let's consider a toy model of a muscle: many springs connected in different ways.

Since we are modeling with springs and metal springs do not contract on their own, let's think about how they respond to being pulled rather than to pulling. The result is the same except for the direction (signs) of the tension forces. We could construct a mechanical model that would pull, but this model is more straightforward to think about.

We'll take as our basic element a single spring (model of a fiber) with rest length ℓ0 and spring constant, k, as shown in the figure at the right. If it is pulled from opposite directions by a tension force, T, it will stretch an amount Δℓ that satisfies the equation

T = kΔℓ

where its stretch length = ℓ0 + Δℓ.