Anatomy, Muscle Mechanics, and Neural Fundamentals for Arm Biomechanics

Anatomy of the Arm

The structure including humerus, radius, ulna, deltoid, scapula, clavicle; basis of biomechanical modeling.

Muscle

A bundle of muscle fibers containing actin and myosin; generates force by contraction.

Muscle Fiber

Individual cells in a muscle that contract using actin-myosin interactions.

Actin

Thin contractile protein that slides past myosin during muscle contraction.

Myosin

Thick contractile protein generating force when interacting with actin.

Tendon

Fibrous tissue attaching muscle to bone; transmits muscle force.

Parallel Fibers

Muscle fibers arranged side by side; more parallel fibers = greater force.

Force Development

Generation of tension in muscle; results from contraction pulling bones.

Free Body Diagram

A simplified drawing showing all forces acting on the arm system.

Static System

A system where sum of forces and torques = 0; no acceleration occurs.

Newton's First Law

ΣF = 0 and Στ = 0 for static equilibrium.

ΣFx = 0

Sum of horizontal forces must equal zero in static equilibrium.

ΣFy = 0

Sum of vertical forces must equal zero in static equilibrium.

Στ = 0

Sum of torques about a pivot must equal zero.

Torque (τ)

Rotational equivalent of force; τ = r × F; increases with distance from pivot.

Moment Arm

Perpendicular distance from pivot to line of action of the force.

Shoulder Joint

Fulcrum/pivot point for static arm model torque calculations.

Fload

Weight held in the hand; produces a downward torque.

Farm

Weight of the arm; acts at its center of gravity (L/2).

Fdelt

Force generated by the deltoid muscle to hold/raise the arm.

Fshoulder

Net reaction forces of the shoulder muscles/joint.

Deltoid Muscle

Shoulder muscle responsible for lifting the arm; small insertion angle increases required force.

Angle of Insertion (θ)

Angle between deltoid force direction and humerus; determines effective torque.

Insertion Point

Location where deltoid attaches; assumed L/4 from shoulder.

Arm Length (L)

Distance from shoulder to hand; affects torque created by loads.

Arm Diameter (2r)

Used to approximate the volume and weight of the arm.

Arm Shape Assumption

Typically simplified to a cylinder for mass estimation.

ρ (rho)

Density of tissue; used to estimate total arm mass: ρ × Volume.

Volume (arm)

πr²L for cylindrical approximation used in Farm calculations.

Center of Gravity

Point where arm weight acts; typically at L/2.

Torque Equation

τ = rF sin θ; used for deltoid torque and external load torque.

Deltoid Torque Eq.

τdelt = Fdelt × (L/4) × sin θ.

Load Torque

τload = Fload × L.

Arm Torque

τarm = Farm × (L/2).

Equilibrium Equation

Fdelt = (2Farm + 4Fload) / sin θ.

Cross-Sectional Area

Determines muscle's maximum force capacity.

Force per Unit Area

Deltoid muscle produces ~30-40 N/cm² (50 lb/in²).

Simulation

Graphing Fdelt vs. Fload to test model sensitivity.

Model Assumptions

Arm geometry, muscle angle, insertion point, uniform density, etc.

Validation

Comparing computed Fdelt to physiological capacity.

Achilles Tendon Model

Another static torque example using foot geometry.

Achilles Tension (T)

Force needed in tendon to counteract foot load and produce torque.

Vector Forces

Forces include magnitude + direction; represented with arrows.

Static Stance

Assumption for Achilles model: body is not accelerating.

Neuron

Basic signaling cell of the nervous system; sends information in one direction.

Dendrites

Branch-like structures receiving signals from other neurons.

Cell Body (Soma)

Contains nucleus; integrates incoming signals.

Axon Hillock

Trigger zone for action potentials; site of summation.

Axon

Long process transmitting electrical impulses away from soma.

Synapse

Junction where axon terminal communicates with another neuron.

Myelin

Insulating sheath increasing conduction speed.

Nodes of Ranvier

Gaps in myelin enabling saltatory conduction.

One-way Flow

Information travels dendrite → soma → axon hillock → axon → synapse.

Convergence

Many neurons synapse onto one neuron.

Divergence

One neuron synapses onto many neurons.

CNS

Central Nervous System; brain and spinal cord.

PNS

Peripheral Nervous System; afferent + efferent neurons.

Afferent Neurons

Carry sensory information to CNS.

Efferent Neurons

Carry motor commands from CNS.

Somatic NS

Controls voluntary skeletal muscle movements.

Autonomic NS

Controls involuntary functions (heart, vessels, glands).

Gray Matter

Neuron cell bodies; outer brain layer, inner spinal cord.

White Matter

Myelinated axons; inner brain, outer spinal cord.

Brodmann Areas

52 cortical regions defined by cellular structure.

Primary Motor Cortex

Region controlling voluntary movement.

Primary Somatosensory

Region receiving touch, pressure, and stretch info.

Visual Cortex

Region in occipital lobe responsible for vision.

Auditory Cortex

Temporal lobe region for sound processing.

Wernicke's Area

Language comprehension center.

Broca's Area

Speech production center.

Reflex Arc

Rapid, involuntary response requiring afferent + efferent neurons.

Interneuron

Modulates reflex by inhibiting or exciting motor neurons.

Knee Jerk Reflex

Stretch muscle → ↑ afferent firing → extensor contracts; flexor inhibited.

Muscle Spindle

Stretch receptor monitoring muscle length.

Alpha Motor Neuron

Efferent neuron causing muscle contraction.

Inhibitory Interneuron Reduces firing of opposing muscle groups.

Stretch Reflex

Negative feedback loop maintaining constant muscle length.

Negative Feedback

Output reduces original stimulus; stabilizes system.

Firing Rate

Frequency of action potentials; encodes stimulus intensity.

Resting Membrane Pot. Baseline neuron voltage (~ -70 mV) determined by ion gradients.

Chemical Gradient

Difference in ion concentration across membrane.

Electrical Gradient

Charge difference across membrane.

Electrochemical Grad. Combined chemical + electrical force driving ion movement.

Nernst Potential

Voltage where net ionic movement = 0 for a specific ion.

Nernst Equation

Ex = -61/z * log([Xi]/[Xo]); determines equilibrium potential.

ENa

Sodium Nernst potential ≈ +60 mV.

EK

Potassium Nernst potential ≈ -90 mV.

Conductance (g)

Permeability to an ion; inverse of resistance.

Chord Conductance Eq. Vm = (gK/gT)EK + (gNa/gT)ENa + ... ; weighted average of ion potentials.

Dominant Ion

Ion with highest conductance determines resting Vm (usually K+).

Graded Potential

Small voltage changes; diminish over distance; input signals.

EPSP

Excitatory postsynaptic potential; depolarizes cell.

IPSP

Inhibitory postsynaptic potential; hyperpolarizes cell.

Temporal Summation

Input signals occurring closely in time add together.

Spatial Summation

Inputs from multiple synapses add together.

Threshold

Voltage required to trigger an action potential.

Neurotransmitter Bind Opens ion channels causing EPSP or IPSP.

Receptor Type Effect

Same neurotransmitter can cause EPSP or IPSP depending on receptor.

Action Potential

Rapid, all-or-none reversal of membrane potential.

Depolarization

Vm becomes more positive due to Na+ influx.