BME 316 Biomechanics Midterm (Exam 1)

Biomechanics

Application of engineering mechanics to understand biological systems (this course: the musculoskeletal system)

Kinematics

Describes spatial and temporal components of motion WITHOUT considering forces

Kinetics

Study of the forces that cause or change motion

Statics

Branch of mechanics where the system has NO acceleration (ΣF = 0, Στ = 0)

Dynamics

Branch of mechanics where the system IS accelerating

Qualitative analysis

Describes motion by observation, no numbers

Quantitative analysis

Describes motion with measured numbers (e.g., force plate, motion capture)

Force plate measuring a long jump is...

Quantitative and Kinetic

Linear motion (translation)

All points move the same distance in the same direction

Curvilinear motion falls under...

Linear kinematics (linear does not have to mean a straight line)

Angular motion

Rotation about an axis

General motion

Combination of linear + angular motion. Most human movement is general motion.

Fixed reference system

Reference frame fixed to the environment

Relative (moving) reference system

Reference frame attached to a body segment or joint

Scalar

Magnitude only (mass, time, distance, speed, height)

Vector

Magnitude AND direction (force, weight, displacement, velocity, acceleration, torque)

Anatomical starting position

Standing erect, arms at sides, palms facing FORWARD (forearm supinated)

Fundamental starting position

Like anatomical, but palms face the body (NO wrist supination)

Superior / Inferior

Toward the head / away from the head

Anterior / Posterior

Toward the front / toward the back

Medial / Lateral

Toward the midline / away from the midline

Proximal / Distal

Closer to / farther from the trunk (on limbs)

Ipsilateral

On the same side of the body

Contralateral

On opposite sides of the body (e.g., right hand and left shoulder)

Axial skeleton

Head, neck, and trunk

Appendicular skeleton

Upper and lower limbs (e.g., the foot)

Sagittal plane

Divides body into left and right; rotation about the medial-lateral axis; flexion/extension (walking, squats)

Frontal (coronal) plane

Divides body into front and back; rotation about the anterior-posterior axis; abduction/adduction (jumping jacks)

Transverse (horizontal) plane

Divides body into top and bottom; rotation about the superior-inferior (longitudinal) axis; rotations (golf swing, spinning)

Plane-axis rule

The axis of rotation is always PERPENDICULAR (orthogonal) to the plane of motion

Medial-lateral axis is orthogonal to which plane?

Sagittal plane

Anterior-posterior axis is orthogonal to which plane?

Frontal plane

Superior-inferior axis is orthogonal to which plane?

Transverse plane

Human walking occurs primarily in the...

Sagittal plane

Golf swing occurs primarily in the...

Transverse plane

Flexion and extension occur in the...

Sagittal plane

Abduction and adduction occur in the...

Frontal plane

Degrees of freedom (DOF)

Number of independent coordinates needed to describe a motion

DOF of a free rigid body

6 (3 translational: x, y, z + 3 rotational: θx, θy, θz)

Max rotational DOF at a joint

3

Hinge joint

1 DOF (knee; humeroulnar part of the elbow). The professor counts the whole elbow as 2 DOF

Pivot joint

1 DOF

Saddle joint

2 DOF (thumb)

Ball-and-socket joint

3 DOF (hip, shoulder): maximum mobility

Elbow joint DOF and movements

2 DOF per the key: flexion/extension + internal/external rotation (pronation/supination); no abduction

Lever

Rigid body that rotates about a fixed point (fulcrum). Body: bone = lever, joint = fulcrum, muscle = effort

Four components of a lever

Rigid body, fulcrum, effort force, load force

Load in human movement can be...

An external object, the weight of the limb, or tension in an opposing muscle

1st class lever

Fulcrum between effort and load (seesaw; head nodding on the neck)

2nd class lever

Load between fulcrum and effort; HIGH mechanical advantage (wheelbarrow, nutcracker, nail clippers, tiptoe raise)

3rd class lever

Effort between fulcrum and load; mechanical DISADVANTAGE but gains speed and range of motion (biceps at the elbow, fishing pole)

Most common lever class in the body

3rd class

Why is biceps force much greater than the weight held?

Torques balance, not forces; the biceps moment arm (~4-5 cm) is much smaller than the load's moment arm

Force

A push or a pull; F = ma; units N (kg·m/s²); vector

Torque (moment of force)

Rotating effect of a force: τ = F × d⊥ (N·m); vector; CCW = positive, CW = negative

Moment arm

PERPENDICULAR distance from the line of action of a force to the axis of rotation (= r sinθ)

Two ways to increase torque

Increase the force or increase the moment arm

Hooke's law

F = kx (spring force is linear with stretch); skeletal muscle does NOT necessarily obey it

Stress (σ)

Force applied to deform a structure; force per unit area; σ = F/A (N/m² or Pa)

Strain (ε)

Deformation caused by applied force; ε = ΔL/L

Elastic modulus

Stress/strain = slope of the stress-strain curve = STIFFNESS of a material (not strength)

Elastic region

Structure returns to original shape when load is removed

Yield point

Boundary between the elastic and plastic regions

Plastic region

Past yield: residual strain, permanent deformation, microtears and debonding

Loading continued past the yield point causes...

Residual strain, plastic response, permanent deformation (all of the above)

Failure

Continued loading past the plastic region; tissue breaks

Strength (of a material)

Failure point / load sustained before failure; energy = area under the stress-strain curve

Elastic material

LINEAR stress-strain relationship

Viscoelastic

NONLINEAR stress-strain; response depends on RATE and DURATION of loading

Hysteresis

Energy lost in a viscoelastic material when the load is removed

Anisotropic

Response depends on the DIRECTION of load application

Bone mechanical properties

Anisotropic and viscoelastic; stiffer and stronger when loaded quickly; slides say bone is 'flexible and weak'

Skeleton % of body weight

About 20%

Functions of the skeleton

Leverage, support, protection, storage, blood cell formation

Skeletal functions critical for movement

Support and leverage

Wolff's law

Bone remodels in response to stress: resorption and deposition

Resorption

Bone breakdown from decreased stress (disuse, immobilization, microgravity); osteoclasts dominate

Deposition

Bone formation from increased stress (weight-bearing exercise); osteoblasts dominate

Osteoporosis

Resorption exceeds deposition; caused by hormonal factors (menopause), low calcium, lack of exercise

Stress fracture

Resorption weakens bone and deposition occurs too slowly; from repetitive loading and muscle fatigue; ~10% of athlete injuries

Cartilage

Firm flexible tissue, no blood supply or nerves; increases joint stability, distributes load, reduces contact stress

Ligaments

Connect bone to bone; collagen, elastin, reticulin; viscoelastic; stronger and stiffer with loading

Synovial (diarthrodial) joint

Low friction, high resistance to wear and tear

Joint stability is created by...

Ligaments, gravity, vacuum (plus muscles dynamically)

Carrying angle

With elbow extended, the angle between the ulna and humerus (forearm angles away from the body)

Fascicle

A bundle of muscle fibers

'Flexing a muscle' is technically wrong because...

Muscles are activated/contract; flexion is a joint movement

Parallel muscle fibers

Fibers parallel to the tendon (biceps brachii, sartorius, rectus abdominis): more range and speed

Pennate muscle fibers

Fibers at an angle to the tendon (unipennate, bipennate, multipennate; rectus femoris, gastrocnemius): more FORCE

PCSA

Physiological cross-sectional area: measured perpendicular to the muscle FIBERS; predicts force

ACSA

Anatomical cross-sectional area: measured perpendicular to the TENDON (long axis)

Why pennate muscles generate more force

More fibers attach to the tendon, so PCSA (more force units in the same space) goes up

Force transmitted to tendon (pennation)

F_tendon = F_fiber × cos(α), where α = pennation angle

Sarcomere

Basic contractile unit of muscle (actin + myosin)

Cross-bridge

A myosin head bound to actin; the ONLY source of active muscle force; forms only when the muscle is activated

Sliding filament theory

A.F. Huxley; explains production of tension: myosin and actin form cross-bridges and slide past each other, so the sarcomere shortens

Hill's muscle model

A.V. Hill, 3 components: contractile (CC), parallel elastic (PEC), series elastic (SEC). NO plastic component.

Contractile component (CC)

Converts stimulation into force

Parallel elastic component (PEC)

Allows muscle to be stretched; associated with fascia around the muscle

Series elastic component (SEC)

Transfers muscle force to bone (tendon)