2 Mechanics of the Body

Forces and linear motion

Biomechanics applies mechanics to living bodies. It explains how forces produce movement and how bones, muscles, tendons, joints, and medical devices carry loads. Unlike a perfectly rigid machine, the body deforms, and tissue behavior can depend on the direction and duration of loading.

A force is a push or pull with magnitude and direction. Muscles create tension that travels through tendons to bones; gravity and contact with the ground or objects provide external forces. Newton's second law relates the net force on an object to its mass and acceleration:

When the net force is zero, there is no linear acceleration: an object remains at rest or continues at constant velocity. While standing still, for example, the floor's upward force balances the body's weight. During walking, forces from the ground help support and accelerate the body.

A free-body diagram is a useful first step in analyzing a body part or device. Isolate the object, then show every force acting on it. For a forearm holding a weight, the diagram could include the weight's downward force, the forearm's weight, the muscle's pull, and forces at the elbow joint.

Takeaway: Identify all forces and their directions before analyzing how a body part moves or balances.

Torque and body levers

Forces can also cause rotation. The turning effect about a joint or pivot is torque:

where $r$ is the distance from the pivot to the force's application point, $\theta$ is the angle between the position and force directions, and $r_{\perp}$ is the perpendicular lever arm. A force generally produces more torque when applied farther from the pivot or more nearly perpendicular to the limb.

Bones act as levers, joints as pivots, and muscles provide applied forces. Many muscles attach close to a joint, so their lever arm is shorter than the lever arm of the external load. This arrangement supports rapid limb movement, but it can require a muscle to exert a much larger force than the load it moves.

Example: A person holds an object with a downward force of $20\,\mathrm{N}$ at a distance of $0.30\,\mathrm{m}$ from the elbow. The object's torque is

If an elbow muscle acts with a lever arm of $0.04\,\mathrm{m}$, it needs a force of about

to balance that torque. This estimate ignores the forearm's weight and other forces. The large muscle force results from its short lever arm.

For a body part that is not rotating, the net torque about a chosen pivot is zero. A nonzero net torque changes angular motion, just as a nonzero net force changes linear motion.

Takeaway: To compare rotational effects, consider both the force and its perpendicular distance from the pivot.

Tissue loading and deformation

A force distributed over an area creates stress, and the resulting relative deformation is strain. For a uniform tensile or compressive load:

Stress is measured in pascals, while strain is dimensionless. Here, $F$ is the applied force, $A$ is the loaded area, $\Delta L$ is the change in length, and $L_0$ is the original length.

Within a material's linear elastic range, stress is proportional to strain. Young's modulus describes that relationship for stretching or compression: a higher modulus means less deformation for a given stress. Elastic deformation is largely reversible once the load is removed. If loading goes beyond a tissue's elastic range, deformation may become permanent or the tissue may fail.

Biological tissues are more complex than ideal springs. Their behavior can vary with direction, may be nonlinear, and can change with time under load. For that reason, one elastic-modulus value cannot fully predict how a tissue will respond to every loading condition.

Load size, direction, and duration all matter. A sudden impact can produce a high peak load, while repeated loading can also contribute to tissue injury. Internal forces are often estimated with measurements and mechanical models rather than measured directly.

Takeaway: Stress describes loading per area; strain describes relative deformation. Tissue response depends on more than a single stiffness value.

Medical devices and mechanical design

Medical devices interact mechanically with the body, so their design must account for force, lever arms, motion, and tissue loading.

• Crutches and canes provide external support and change how forces are distributed among the hands, arms, legs, and ground.

• Prosthetic limbs transmit loads while providing useful movement. Their geometry and alignment affect the torques required during activities such as walking.

• Orthoses and braces guide or limit joint motion and transmit forces between the device and the body.

A device should provide its intended support while fitting the person and avoiding excessive or poorly distributed pressure. Biomechanical models and motion measurements can help evaluate movement and device performance.

Takeaway: Effective mechanical design connects the device's support and movement goals with the forces and pressures experienced by the body.