Unit 5: Mechanics of shoulder, spine and hip

BTY730 — Biomechanics 7 min read

Biomechanics of the shoulder, spine and hip treats each region as a system of rigid bones linked by joints, actuated by muscles and constrained by ligaments, then applies Newtonian statics to resolve the forces and moments they carry. These three regions share the analytical toolkit developed for joints generally but differ sharply in their trade-off between mobility and stability.

Free-body diagram (FBD): the working method throughout: isolate a segment, mark external loads (gravity, hand load), joint reaction and muscle force, then apply equilibrium.
Static equilibrium conditions: with no acceleration,
TEXT
```
  ΣF = 0      ΣM = 0
```
where F are forces (N) and M are moments (N·m); moments are taken about the joint centre.
Muscle moment arm (d): the perpendicular distance (m) from the joint axis to a muscle's line of action; small moment arms force large muscle and joint reaction forces.
Joint reaction force (J): the net contact force between articulating surfaces, found last from ΣF = 0 after the muscle force is known.
Mobility–stability trade-off: the shoulder favours mobility (shallow socket), the hip favours stability (deep socket), the spine balances both segmentally.

II. Mechanics of the Shoulder

The most mobile and least stable major joint complex.

A. Structure of the shoulder

The shoulder is a complex of four articulations acting together, not a single joint.

Glenohumeral (GH) joint: ball-and-socket between the humeral head and the scapular glenoid fossa; the glenoid covers only about a third of the head, giving 3 rotational degrees of freedom but little bony containment.
Acromioclavicular and sternoclavicular joints: link the clavicle as a strut between sternum and scapula, positioning the glenoid in space.
Scapulothoracic articulation: a functional (not true) joint where the scapula glides on the thorax.
Stabilising soft tissue: the glenoid labrum deepens the socket ~50%; the rotator cuff (supraspinatus, infraspinatus, teres minor, subscapularis) compresses the head into the glenoid; the glenohumeral ligaments and joint capsule resist extremes.

B. Movements of shoulder complex

Arm elevation is produced by coordinated motion at all four articulations, not the GH joint alone.

GH degrees of freedom: flexion/extension, abduction/adduction, internal/external rotation.
Scapulohumeral rhythm: for full ~180° abduction, motion divides roughly 2:1 — about 120° at the GH joint and 60° of scapular upward rotation.
Force couples: deltoid and supraspinatus form a couple at the GH joint — deltoid pulls the head upward, the cuff pulls it inward and down, keeping the resultant centred.
- Scapular couple: upper and lower trapezius with serratus anterior rotate the scapula upward.
Consequence: disrupting the cuff lets the deltoid shear the head superiorly against the acromion (impingement).

C. Loads on the shoulder

Because muscle moment arms are short relative to the load arm, GH joint forces greatly exceed the weight held.

Model: treat the abducted arm as a lever about the GH centre; deltoid acts at a small moment arm, arm weight at a long one.
Order of magnitude: at 90° abduction the GH reaction reaches roughly the body weight even with no hand load, and multiples of it when lifting.
Worked example (arm held at 90°):
TEXT
```
  Arm weight W = 40 N at moment arm a = 0.30 m
  Deltoid moment arm d = 0.03 m
  ΣM: F_d · 0.03 = 40 · 0.30
  F_d = 12 / 0.03 = 400 N
```
The deltoid must pull ~400 N — ten times the limb weight — so the joint reaction is correspondingly large.

III. Mechanics of the Spine

A segmented column balancing load transmission, protection and mobility.

A. Structure of the spine

The spine is a stack of vertebrae and intervertebral discs forming a curved, load-bearing column enclosing the cord.

Regions and curves: 7 cervical, 12 thoracic, 5 lumbar, plus sacrum and coccyx; cervical and lumbar lordosis, thoracic kyphosis — the curves act as a leaf-spring, raising axial load tolerance.
Functional spinal unit (motion segment): two adjacent vertebrae plus the disc and ligaments — the smallest unit showing spine-like mechanics.
Intervertebral disc: central gelatinous nucleus pulposus pressurised inside the fibrous annulus fibrosus; the nucleus behaves hydrostatically, converting axial compression into hoop tension in the annulus.
Facet (zygapophyseal) joints: posterior joints whose orientation dictates permitted motion — near-sagittal in the lumbar spine (favouring flexion/extension), oblique in the thoracic (favouring rotation).
Ligaments: anterior/posterior longitudinal, ligamentum flavum and interspinous ligaments limit range and store energy.

B. Movements of the spine

Small motions summed across many segments give large overall range.

Degrees of freedom per segment: flexion/extension, lateral bending, axial rotation, plus small translations.
Regional bias: lumbar spine — large flexion/extension, little rotation; thoracic spine — large rotation, limited flexion (rib cage constraint); cervical spine — the most mobile in all directions.
Instantaneous axis of rotation (IAR): the momentary pivot within the disc; it migrates during motion, and abnormal IAR paths indicate instability.
Coupled motion: lateral bending is mechanically linked to axial rotation, especially in the cervical and lumbar regions.

C. Muscles and loads on the spine

The short moment arms of the erector spinae force very high compressive loads during forward lifting.

Extensor musculature: erector spinae act ~5 cm posterior to the disc; because the trunk load acts far anteriorly, the muscle force needed is large.
Intra-abdominal pressure (IAP): contracting abdominals pressurise the trunk cavity, creating an extensor moment that offloads the spine.
Cantilever model of lifting: the trunk is a lever pivoting at L5–S1; upper-body weight and any hand load create a large flexion moment resisted by erector spinae.

Worked example (stoop lift):

TEXT

  Load moment (trunk + object) M_ext = 200 N·m about L5–S1
  Erector spinae moment arm d = 0.05 m
  Muscle force F_m = 200 / 0.05 = 4000 N
  Compression ≈ F_m + axial component of external load ≫ 4000 N

Disc compression easily exceeds several thousand newtons, which is why lifting technique and IAP matter.

Posture effect: compressive disc load is lowest lying, moderate standing, and highest sitting slumped and leaning forward.

IV. Mechanics of the Hip

A deep ball-and-socket joint built for stable weight-bearing.

A. Structure and movements of the hip

The hip trades the shoulder's mobility for bony stability suited to gait and standing.

Articulation: femoral head in the deep acetabulum, further deepened by the acetabular labrum; the head is nearly fully enclosed, giving intrinsic stability.
Bony geometry:
- Neck-shaft angle (~125°): angle between femoral neck and shaft; excess (coxa valga) or deficit (coxa vara) alters load distribution.
- Anteversion (~15°): forward twist of the neck relative to the femoral condyles.
Capsule and ligaments: iliofemoral (Y) ligament — the strongest in the body — resists extension and stabilises upright stance.
Movements: flexion/extension, abduction/adduction, internal/external rotation and circumduction; flexion range is largest, extension the smallest.
Muscle groups: gluteus maximus (extension), gluteus medius/minimus (abduction, pelvic stabilisation), iliopsoas (flexion), adductor group, and the deep external rotators.

B. Loads on the hip

Single-leg stance loads the hip far above body weight because the abductors act at a short moment arm to balance the pelvis.

Frontal-plane balance: in one-legged stance the body weight acts medial to the hip while gluteus medius pulls laterally at a shorter moment arm, so the abductor force exceeds body weight.
Lever ratio: the abductor moment arm is roughly half the body-weight moment arm, so abductor force ≈ 2× the supported weight; the joint reaction then sums both and reaches ~3× body weight in level walking.

Worked example (single-leg stance):