Levers, moment arms and contact

Companion to chapters 5, 6, 12 and 22 of Human Biology for the Medical Maker: Bones, joints and movement, Tissues and contact, Lifespan and mind and the capstone elbow model. Educational only — not a medical device, and not for diagnosis, treatment, monitoring or dosing.

How to use it

Elbow lever. A two-strip model like the book’s capstone: the upper-arm strip is fixed and vertical, the forearm strip turns about the pivot, and a cord runs from an attachment on the forearm through a guide on the upper arm. Drag the forearm end to set the flexion angle (0° hangs straight down, 90° is horizontal), and drag the attachment A, the load L and the guide G — or type the values; the 20/40/60 mm buttons are the chapter 6 workshop positions.

Cord through guide is the real geometry: the moment arm is the perpendicular distance from the pivot to the cord’s line of action, d⊥ = a·g·sinφ ÷ √(a² + g² + 2ag·cosφ), not the distance along the strip; gravity acts straight down, so a load’s torque is F·d·sinφ. The cord pulled per degree equals d⊥ in radians (virtual work), which is why a closer attachment gives more swing per millimetre of cord and needs more force.
Idealised (book) makes every force perpendicular to the forearm, so d⊥ is the attachment distance at every angle. The preset buttons reproduce the book’s worked examples: 2 N at 0.20 m with a 0.04 m arm is 0.40 N·m and 10 N; with a 1.4 kg forearm at 0.14 m and 2 N at 0.33 m the book gets 64.4 N (it rounds the weight to 13.7 N first; from 1.4 kg × 9.81 the tool shows 64.6 N); appendix E’s 3 N at 0.10 m with 0.03 m is 10 N.
Segment weight can be a mass and centre of mass you type, or Winter’s anthropometric fractions — forearm and hand 2.2 % of body mass, centre of mass 0.682 of the elbow-to-ulnar-styloid length (D. A. Winter, Biomechanics and Motor Control of Human Movement, 4th ed., Table 4.1). Those are population averages, not any one person.
The sweep plots the moment arm, the cord force with and without segment weight, and the cord travel per degree from 5° to 175°. The pivot reaction shows why internal joint forces exceed the external load.
The lever class (first, second or third) follows from where the effort and the load sit relative to the pivot. A negative load distance puts the load behind the pivot.

Every result has its assumptions printed beside it. They are the point: the book uses this arithmetic to show why attachment geometry matters, never to specify a force for a person.

Contact pressure. p = F ÷ A, in kPa, mmHg (1 mmHg = 133.322 Pa) and N/cm², from an area or a rectangle or circle. The book’s example — 20 N over 10 cm² — is 20 kPa, about 150 mmHg. A second calculator puts a share of the force through a small feature (a seam, a ridge, a screw head) to show how an average hides a local peak. The list of what the calculation cannot tell you — distribution, depth, time, the person, movement — is always on screen, and the tool offers no threshold: chapter 5 is explicit that published interface-pressure figures are not yours to apply.

Falls. E = m·g·h, the speed at impact, and the average force E ÷ d over a stopping distance — the same energy stopped over less distance gives more force. A 70 kg person whose hip drops 0.9 m carries about 620 J (chapter 12); a 20 cm bed carries under a quarter of that. The table compares a low bed, a chair seat and standing.

Stiffness and strength of tissues against engineering materials moved to tissues, materials and temperature.

Limits

Statics only: no acceleration, friction or soft-tissue compliance; one force path where real joints share load between muscles in a way statics cannot resolve.
The elbow model is a card-strip teaching model. Its guide position is a model convenience, not an anatomical tendon route, and its pivot has a fixed centre where a real elbow’s moves.
Fall forces are upper bounds: all the energy is assumed to go into one contact, and the result is an average, not the peak. Nothing here says whether an injury would happen.
Average pressure is not peak pressure, nor the stress deep in tissue.

Related: tissues, materials and temperature (stiffness, polymer temperatures, expansion), batch, tolerance and shelf life, physics calculators (forces, energy), springs.

Share link (under the title) copies a URL that reopens this tool exactly as you have it — every tab’s inputs, with the current tab selected. Each tab has its own address: #contact or #falls opens that tab. Opening such a link replaces the inputs this browser had saved for the tool.

How to use it

Limits

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