toys & demonstrators

This page is both a gallery of ‘low fidelity physical demonstrators’ relating to the science presented on the other pages, and a source for teaching materials. Do email me at for the latest versions.

Linkage legs

Laser-cut lollipop dog forelimb

Three linkages resulting in sliding weight support (see THIS PAGE). In early stance, the long head of the triceps brachii is under tension forming a 4-bar linkage and coupling retraction with leg shortening. In midstance the lateral head of the triceps brachii comes under tension, and the whole leg vaults. In late stance, the supraspinatus comes under tension, releasing the short head triceps, and allowing rotation about the elbow; the leg extends in late stance without requiring elastic recoil.

Outlines for laser-cut parts are available:

Snap rivets are used here, but split-pins or brads are also effective (see below).

Laser-cut lollipop sprinter

The same three linkages but loading in reverse order applies to human sprinting. In early stance, the gluteus is under tension and, before the vastus comes under tension, allows the knee to vault over the foot; the leg shortens in early stance with forces directed ahead of the hip, but without elastic deflection. In midstance the vastus locks the knee and the hip vaults about the foot. In late stance, the rectus femoris acts as a link in a 4-bar linkage, coupling retraction with leg extension. Forces project behind the hip, and (in this model) the leg extends entirely without elastic recoil.

The laser-cut parts are those for the dog forelimb. The card background is here. It is A4 format; be careful not to allow the printer to autoscale.

Quadruped hindlimb practical

A practical that leads the student through the geometry of how and why muscles can be automatically and sequentially loaded under isometric to produce sliding weight support through producing a straight-line mechanism. Dimensions are for lollipop sticks and A4 card.

Animation of a practical in which hindlimb muscle geometry is calculated that results in sliding weight support

A very brief introduction (with audio) here

1 minute introduction to hindlimb linkage leg

Instructions follow. Again, designed around standard and large lollipop stick and A4 dimensions; be careful not to rescale when printing. Muscles look good if printed on red paper.

Lego ant

The remarkable force measurements of ants HERE and HERE show that insect legs can also achieve the economical ‘sliding’ condition, with approximately vertical forces during horizontal translation. This Lego demonstrator shows how 4-bar linkages can be combined with vertical-axis joints (discussed in THIS PAPER) to result in a tripod of support over which the body is free to slide. Of course, insect legs are actually far more complicated; this just demonstrates that sliding weight support with legs is achievable with very simple linkages.

Lego WoodAnt

Lego horse

This Lego demonstrator combines both the Roberts mechanism model of the serratus supporting the forelimb, and two 6-bar linkages of the hindlimb. The linkages enable approximately horizontal ‘sliding’ motion, with the legs getting functionally shorter over the first half of stance and longer over the second. But nothing is ‘stretching’ – the shortening and lengthening of the legs is due to the linkages, not because of elastic deflection and recoil.