Welcome to chapter six, bones, joints and movement. This is the chapter where your existing engineering knowledge is most useful and most dangerous at the same time. Joints really are pivots, muscles really do apply forces, tendons really are tension members, and the statics you already know is the right statics. But the simplification of joint as hinge, muscle as linear actuator and tendon as cable is close enough to be convincing, and wrong in ways that matter. By the end of this session you should know exactly where that model holds and where it breaks.
On the left is what transfers directly from the workshop. A free-body diagram of a forearm is a genuine free-body diagram. On the right is what breaks the simple model. Real joints have centres of rotation that move as the joint bends. Real muscles produce force that depends on their length and on how fast they are moving. Real tendons wrap over surfaces whose geometry changes the moment arm continuously through the motion. And a person's comfortable, repeated range is a different number from their maximum range, which is different again from what a diagnosis might lead you to assume.
Bone is a composite. A collagen matrix gives it toughness and tensile strength, and a calcium phosphate mineral called hydroxyapatite gives it stiffness in compression. Neither alone would do. It comes in two forms. Cortical bone is the dense outer shell and the shafts of long bones, carrying bending and torsion. Trabecular bone is an open lattice of struts inside the ends of long bones and the vertebrae. If you have ever designed a lattice infill, trabecular bone is what you were imitating: its struts really do align with the principal stress directions. And it is alive. Cells called osteoblasts build, osteoclasts resorb and osteocytes sense, so the structure is rebuilt continuously.
Here is the practical consequence of remodelling. Bone responds to the load it carries. Unload it, through bed rest, spaceflight, a cast, or an implant that takes the load the bone used to take, and it loses mass. That is why stress shielding is a central concern in orthopaedic implant design, and why stiffer is better is simply false in that context. A stiffer implant takes more of the load, so the bone takes less, so the bone weakens. It is a good example of a design principle that is correct in a bridge and wrong in a body.
These are literature ranges, not design values, but they put you in the right decade. Cortical bone has a stiffness of fifteen to twenty gigapascals. Trabecular bone varies over more than two orders of magnitude depending on site and density. Titanium alloy is the closest common metal to bone, which is part of why it is used in implants, while stainless steel is about ten times stiffer than cortical bone. The genuinely useful fact here is that bone is anisotropic, considerably weaker across the grain than along it. And so is almost everything you make. A printed part is weakest between layers, a fibre-filled moulding is stiffer along the flow, wood follows its grain, and a weld differs from the parent metal. Orientation is a structural decision.
You do not need to memorise all two hundred and six bones. Learn the ones in the region your project touches, plus enough of the rest to place a conversation. The axial skeleton is the skull, the vertebral column and the rib cage. The appendicular skeleton is the shoulder and pelvic girdles and the limbs. Most assistive and training projects involve hands and arms, so the chapter takes the upper limb in detail.
The clavicle, or collarbone, is the only bony strut connecting the arm to the trunk at the front. The scapula glides on the back of the rib cage, and that gliding contributes a large share of what people call shoulder movement. In the forearm, the radius is the lateral bone on the thumb side in anatomical position, and it is the one that rotates for pronation and supination. The ulna is medial, and its olecranon is the point of your elbow. The wrist is eight small carpal bones moving together, not one hinge, and the thumb's saddle-shaped joint at its base is what gives us opposition.
The elbow region contains three articulations inside one capsule. The humeroulnar joint is the main hinge for bending and straightening. The humeroradial joint takes part in that too. And the proximal radioulnar joint lets the radius rotate for pronation and supination. A single-pivot model therefore represents one function of the region. That is a legitimate simplification for a teaching aid whose objective is flexion and extension, but the omission must be stated. Saying this model omits forearm rotation takes four seconds and stops a learner forming a wrong picture.
Almost every joint you will model is a synovial joint. The bone ends are capped with articular cartilage, the joint is enclosed in a fibrous capsule, and an inner synovial membrane secretes the fluid that fills the cavity. Outside that simple picture are ligaments constraining motion, muscles and tendons actively stabilising it, fluid sacs called bursae, pads of fibrocartilage in some joints, and sensory nerve endings. Healthy joint friction is astonishingly low, with coefficients quoted around three thousandths to two hundredths, better than most engineered dry bearings. The mechanism is not a simple fluid film: fluid pressurised inside the cartilage is squeezed out under load, alongside boundary lubrication at the surface.
A metal hinge represents the pivot. It does not represent cartilage, capsule or fluid. It does not represent ligaments constraining the motion, muscles actively stabilising the joint, or the sensory feedback the joint provides. And it does not represent the fact that the centre of rotation moves through the range of motion. Each of those is something your model silently claims does not exist, unless you say otherwise. Writing that list down is not pedantry; it is the honesty that makes a teaching model safe to learn from.
There are six types of synovial joint. Plane joints slide, like the small bones of the wrist. Hinges have one axis, like the elbow and the finger joints. Pivots rotate about a long axis, like the radius turning on the ulna, or your head shaking no. Condyloid and saddle joints have two axes, like your knuckles and the base of your thumb. Ball-and-socket joints have three, like the shoulder and hip. But geometry is not the whole story. The shoulder is a shallow ball and socket with an enormous range, bought at the cost of stability, so it depends heavily on muscle to stay in place. The hip is a deep socket: more stable, less range. It is the same trade-off you make in a mechanism.
Movement has precise names. Flexion generally decreases the angle at a joint; extension increases it. Abduction moves a part away from the midline, adduction toward it. Pronation and supination are the two newcomers get wrong, so anchor them physically. Elbows bent, forearms horizontal: palm up is supination, as in carrying a bowl of soup. Palm down is pronation. The real movement is the radius rotating around the ulna. And beware: if the elbow is straight, the shoulder can rotate and disguise the forearm movement. Ask someone to turn their palm up with a straight arm and you may be measuring their shoulder.
For any joint there are three different numbers. Active range of motion is what the person can achieve with their own muscles. Passive range is what the joint permits when it is moved by an external force. Functional range is what they actually use, comfortably and repeatedly, for a real task. The differences between them are diagnostically meaningful, which is why measuring them is a clinical skill. Moving your own wrist tells you about your wrist, on that day. It does not tell you about anyone else, and it certainly does not license you to move someone else's joint. Forcing a joint can injure it.
These are textbook orientation values for a typical adult. Elbow flexion runs from about zero to a hundred and forty-five degrees, though many daily tasks use only about thirty to a hundred and thirty. Forearm rotation is about eighty to ninety degrees each way. They vary with age, sex, build, activity, injury and measurement method, and published ranges differ between sources. Never design to these numbers for a specific person. Have a therapist measure the person, and then design for less than their maximum, because a design that needs someone's end range will be uncomfortable, tiring and abandoned.
Now muscle, and the one fact a maker needs most from this chapter.
A muscle is built in nested levels: the whole muscle, bundles called fascicles, individual fibres which are single long cells, myofibrils inside them, and repeating contractile units called sarcomeres, made of actin and myosin filaments. Force comes from myosin heads binding actin and ratcheting, the sliding filament mechanism. A nerve signal releases calcium inside the fibre to expose the binding sites, and ATP powers the cycle. Force is graded two ways: recruiting more motor units, and firing them faster. Small precise muscles, like those moving the eye, have just a few fibres per nerve cell, giving fine control; large postural muscles have hundreds.
This is the fact a maker needs most. The motor is the muscle. The tendon is a tension member that transmits the force to bone. They are not the same component, and confusing them is the single most common misconception a simplified joint model creates. The running elbow project in this book exists largely to teach that one distinction well.
A muscle does not have to shorten to produce force. In an isometric contraction it produces force without changing length, like holding a bag still at your side. In a concentric contraction it shortens while producing force, like lifting the bag. In an eccentric contraction it lengthens while producing force, absorbing energy, like lowering the bag slowly or your thigh muscles on a descending stair. Eccentric force can exceed the maximum isometric force. Two design consequences. A task with no movement can still be very tiring, because holding a position is real work. And a model where the muscle only pulls things together has left out the controlled-lowering half, which is when most injuries happen.
Two relationships distinguish muscle from an actuator. The length-tension curve shows that force peaks at an optimal overlap of the filaments; away from it, too short or too long, the same muscle produces less. The force-velocity curve shows that force falls as shortening speed rises. So the force a muscle can produce depends on the joint angle, which sets its length, and on how fast the joint is moving. A maximum grip strength figure is a measurement under particular conditions, not a property of the person.
Muscles work in groups. The agonist, or prime mover, produces the movement: for bending the elbow, the biceps and brachialis. The antagonist, the triceps, opposes it and controls and decelerates the movement. Synergists assist and refine the direction, and stabilisers hold the proximal segment steady so the movement is effective. The antagonist is not the enemy. When agonist and antagonist fire together, called co-contraction, the joint stiffens, which is how you keep a hand steady for delicate work. It also costs energy, which is why precision tasks are tiring.
Now the engineering bridge. This is statics you already know, applied to an arm.
Torque is force times the perpendicular distance from the pivot to the force's line of action. That perpendicular distance is the moment arm, and it is not the distance along the beam to the attachment point. That confusion is the commonest error in a first biomechanics calculation, and it explains why a cable gets less effective as a joint rotates. In the idealised elbow, a two newton load at twenty centimetres makes zero point four newton metres. A cable acting at four centimetres must pull ten newtons to balance it. Halve its moment arm and the force doubles to twenty. That five to one disadvantage is roughly how your own elbow works.
Now a slightly more honest version. Model the forearm and hand as a segment of about one point four kilograms, roughly fourteen newtons, with its centre of mass fourteen centimetres from the elbow, holding a two newton object at thirty-three centimetres, with a muscle moment arm of four centimetres. The muscle force comes out at about sixty-four newtons. The segment's own weight dominates, contributing nearly three times the torque of the object. That is why just holding your arm out is tiring with nothing in your hand, and why a design that demands a sustained unsupported arm position makes a much bigger demand than its designer thinks.
The body is dominated by third-class levers, where the effort sits between the fulcrum and the load. They always have a mechanical disadvantage. The body has optimised for range and speed of movement rather than force efficiency: a small muscle shortening near the joint gives a large, fast movement at the hand. It pays for that with high internal muscle and joint forces. A maker whose instinct is that this is a terrible mechanical arrangement has correctly spotted the trade-off and missed its purpose.
Grips come in several kinds: power, hook, precision pinch, lateral key pinch, tripod and spherical. Published strength figures are useful orientation and dangerous design inputs, for three reasons. The maximum someone can exert once is not what they can produce repeatedly while doing something else. Your users may be nowhere near the population the table was built from; that is often why an assistive device exists. And strength is only one demand among many. The same caution applies to body dimensions. Percentiles are computed per dimension, so there is no ninety-fifth percentile person, and stacking ninety-fifth percentile dimensions produces a shape that fits nobody. Design for a range.
Musculoskeletal medicine is the most mechanical specialty, so your skills in machining, sheet metal, thermoforming, casting, sewing, electronics and mechanism design transfer most directly here. Clinical devices include joint replacements, fracture fixation, orthoses, prostheses and mobility aids, most of them prescribed and highly regulated. Assistive equipment, like grip aids and adapted cutlery, is the classic maker and occupational therapist collaboration. Free software such as OpenSim turns this chapter's statics into a real tool, and pose estimators run on a laptop. On the training side: articulated models, fracture fixation trainers, arthroscopy simulators, and instrumented rigs with load cells and encoders.
The line to watch in this chapter is load bearing. A model that demonstrates movement is a teaching aid. The moment an object supports a person's weight, restricts a joint's movement, or applies force to a limb, it has become an orthosis or a mobility aid: a prescribed clinical device with assessment, fitting, review and regulatory obligations. That transition is easy to make by accident. Could you make it a bit stronger so they can lean on it, is a change of project, not a change of specification.
In the worked example, your elbow model's cord is attached four centimetres from the pivot. Move it to two centimetres and three things change. The force needed roughly doubles. You pull less cord for the same angle, trading force for range, exactly the body's bargain. And the model feels strongest at a different angle. Now the teaching question: what will a learner conclude? Unlabelled, they will conclude the cord is the muscle and it pulls. The repair is labels. The free end you pull is the external input representing muscle action. The cord is a tendon that transmits but does not generate force. The pivot is a simplified joint. And the guide loop is a model convenience, not an anatomical tendon route.
For the workshop, build the two-strip model and always write your prediction before you pull. Vary the attachment point and record what happens to force and to angular sweep. Calculate the cord force to balance a two newton load, stating every assumption, and estimate the error from ignoring the strips' own weight. Write a list of at least eight anatomical features the model does not represent; you will reuse it later. And write a one-page functional brief for a grip aid covering task, user, environment, duration and fatigue, without specifying a material or a process. Keep fingers clear of pinch points, and keep the model off the body.
Finally, the limits. You know the vocabulary of range of motion, but measuring and interpreting it on a person is a clinical skill. The statics is right for an idealised rigid beam; a real limb involves indeterminate muscle sharing, changing geometry and large joint forces, so treat your numbers as orders of magnitude. Splints, braces and anything that takes body weight need clinical involvement from the start, not at review. And your model is one selected relationship, honestly labelled, not an anatomy reference. Next, nerves, sensation and accessible design.