OPBSBiomechanics
Must Know
- Biomechanics applies engineering mechanics to musculoskeletal structure and function.
- Muscles generate joint loads, tendons transmit them and bones withstand them.
- Dynamics splits into kinematics and kinetics, both built on Newtonian mechanics.
- Kinematics. Describes motion (displacement, velocity, acceleration) without regard to the forces causing it.
- Kinetics. Relates motion of a body to the forces and moments causing it.
- Borelli, author of De Motu Animalium, is credited as father of modern biomechanics.
Types of Motion
| Motion | Definition |
|---|---|
| Translation | A line between two points on the body keeps its direction. Rectilinear if paths are straight, curvilinear if curved |
| Rotation | Points move in circles about an axis perpendicular to the plane of motion |
| General motion | Translation and rotation together |
- Degrees of freedom (DOF) are the independent motions needed to define position and orientation.
- An unconstrained rigid body has six DOF, three rotations and three translations.
- Anatomic constraints reduce DOF. DOF plus constraints always total six in three dimensions.
| Joint model | DOF | Example |
|---|---|---|
| Hinge | 1 | Interphalangeal joints, elbow |
| Universal (two hinges at 90 degrees) | 2 | Metacarpophalangeal joint |
| Ball and socket | 3 rotations | Hip |
Planar Motion and the ICR
- Instant centre of rotation (ICR) is the point of zero velocity relative to the rotating points.
- The ICR need not lie on the moving body.
- Velocity method. Perpendiculars to the velocity vectors of two points intersect at the ICR.
- Reuleaux method (1876). Perpendicular bisectors of two point displacements intersect at the ICR.
- A true hinge has a fixed ICR. Added translation makes the ICR move through the arc.
- Centre of curvature is the geometric centre of the articular surface.
| Surface motion | Contact points | ICR | Most wear |
|---|---|---|---|
| Sliding (gliding) | Moving segment point fixed, fixed segment point changes | Centre of curvature of fixed surface, infinity if flat | Moving segment contact point |
| Spinning | Fixed surface point unchanged | Centre of curvature of spinning body | Fixed surface contact point |
| Rolling | Both change, equal arc lengths | At the contact point | Minimal |
- Normal knee flexion combines rolling back with forward sliding, keeping contact on the plateau.
- A single fixed hinge axis cannot reproduce knee motion, which led to the polycentric knee.
More on knee surface motion
- Pure spinning would jam the femoral metaphysis on the posterior tibial rim at about 130 degrees of flexion.
- Pure rolling would roll the femur off the plateau at about 45 degrees, needing a far deeper plateau.
- Knowledge of surface motion informs prosthesis design, wear, stability and diagnosis.
Three Dimensional Motion
- A ball and socket model needs three angles to define orientation.
- Finite rotation is sequence dependent and is not a vector. Order changes final position.
- Codman described this in 1935, now called Codman’s paradox.
- Eulerian angles standardise rotation, with one axis on each segment and a floating axis.
| Knee Euler axis | Fixed to | Motion |
|---|---|---|
| Transcondylar, medial to lateral | Femur | Flexion and extension |
| Tibial shaft | Tibia | Internal and external rotation |
| Floating, orthogonal to both | Neither | Abduction and adduction |
- Six DOF motion is best described by the screw displacement (helical) axis.
- The segment rotates about and translates along one axis at the same time.
- Screw axis orientation does not depend on the reference coordinate system.
- The screw axis avoids gimbal lock, where Euler angles cannot define orientation uniquely.
- Gimbal lock arises at the shoulder when humeral axial rotation aligns with the trunk flexion axis.
More on the screw axis
- Besides rotation and translation, four parameters define the axis inclination and location.
- The screw axis is a true vector, but the finite screw rotation is not, because finite rotations do not commute.
- It can be broken into orthogonal axes that suit decomposition of force and moment vectors.
Kinetics Definitions
- A rigid body has negligible deformation under the applied forces.
- Unbalanced forces or moments produce a dynamic state and motion.
- Forces are contact forces or field forces (gravitational, electric, magnetic).
- A force vector has magnitude, direction, sense and point of application.
- Moment. Force times perpendicular distance from line of action to axis. Direction by right-hand rule.
- Moment arm. Shortest distance from line of action to the pivot.
- Torque. Couple of equal, parallel, opposite forces. Magnitude F times D, net force zero.
- Skeletal motion results from moments produced by muscles crossing joints.
| External forces | Internal forces |
|---|---|
| Contact with objects, gravity, inertia | Muscle, ligament and joint contact forces responding to external load |
- Analyses assume rigid segments and frictionless joints, given the very low cartilage friction.
- Ground reaction force behind the knee gives an external flexion moment, balanced by an internal quadriceps extension moment.
Statics and Free-Body Analysis
- Equilibrium needs sum of forces zero and sum of moments zero.
- Three dimensions need six equations (three force, three moment), matching six DOF.
- Planar problems need three. ΣFx, ΣFy and ΣMz each equal zero.
- Coplanar concurrent forces can be replaced by one resultant force with no net moment.
- A negative solution means the assumed force direction was wrong, not the magnitude.
- Taking moments about the hip centre removes the unknown joint reaction components from the equation.
- Short abductor lever arm makes hip joint reaction force exceed the abductor force.
- Step 1. Draw a free-body diagram including unknown forces.
- Step 2. Choose coordinate axes.
- Step 3. Substitute forces into ΣF = 0 and ΣM = 0.
- Step 4. Solve for the unknowns.
More on the worked examples
- Rotator cuff example. Infraspinatus 75 N at 70 degrees, supraspinatus 100 N vertical, subscapularis 100 N at 60 degrees give a resultant of 258 N at 84.6 degrees.
- Single limb stance example. Body weight 120 lb, limb 18 lb (15 percent), abductors at 60 degrees with a 3 inch lever arm.
- Abductor force solves to 178 lb. Joint reaction components are 89 lb horizontal and 256 lb vertical, acting at 71 degrees.
- Aristotle analysed animal movement and Leonardo da Vinci studied body mechanics before Borelli.
Numbers to Remember
- Rigid body DOF. Six.
- Equilibrium equations. Six in 3-D, three in 2-D.
- Hinge, universal, ball. One, two and three DOF.
- Dates. Reuleaux 1876, Codman 1935.
Memory Aids
- Kinematics is cinema. It films the motion. Kinetics adds the forces.
- Wear goes to whoever keeps the same spot. Sliding wears the moving point. Spinning wears the fixed point.
- Screw beats gimbal. The helical axis avoids gimbal lock and coordinate dependence.
Exam Traps
- Finite rotations are not vectors and do not commute.
- In rolling the ICR sits at the contact point. In pure sliding on a flat surface it is at infinity.
- A torque has zero resultant force.
- The hip is modelled as three rotational DOF, though every real joint has six.
- The MCP joint is the universal joint example, not a hinge.
Related pages. Shoulder Biomechanics, Elbow, Biomechanics of the Foot, Material Properties
Source
Kaufman K. Biomechanics of the Skeletal System. In. Aaron RK, editor. Orthopaedic Basic Science. Foundations of Clinical Practice. 5th ed. Philadelphia, Wolters Kluwer, 2021.
Practise Type X questions on this topic
Reviewed by Professor Phong Tran, Head of Orthopaedic Surgery, Western Health. Last updated 17 October 2026.