Joints, Degrees of Freedom, and Kinematics – Study Notes

Joints, Degrees of Freedom, and Kinematics – Study Notes

Joints

• Joints are designed mainly for stability or mobility.
• Joints are joined by connective tissue structures that must maintain junction integrity while allowing motion between bones.
• The architectural challenge of joints is to balance mobility and stability; there is an inverse relationship between the two: Mobility versus Stability.
• The amount of mobility or stability varies across joints.
  • Skull joints are primarily for stability between articulating bones.
  • Glenohumeral (shoulder) joint allows remarkable mobility with relatively less stability.
• In terms of stability, the main function is to transmit force efficiently.
• Stability can be achieved by:
  • Outside support by ligaments
  • Dynamic force transmission by tendons
  • Cartilage wedges (end bone shapes) that provide bracing and increase congruence

Degrees of Freedom (DOF)

• DOF: The number of ways a joint can move.
• Types of motion considered:
  • Translational Movement
  • Rotational Movement
  • In Three Perpendicular Axes about Three Perpendicular Axes: Heave, Sway, Surge, and Yaw, Roll, Pitch
• Six Degrees of Freedom: 6 DOF, comprising three translational (heave, sway, surge) and three rotational (yaw, pitch, roll).
• A joint can have up to three rotational DOFs:
  • One DoF (uni-axial): Movement in 1 plane around 1 axis
  • Two DoFs (bi-axial): Movement in 2 planes around 2 axes
  • Three DoFs (tri-axial): Movement in 3 planes around 3 axes
• Conceptual mapping:
  • One DoF: Movement in 1 plane & around 1 axis
  • Two DoFs: Movement in 2 planes & around 2 axes
  • Three DoFs: Movement in 3 planes & around 3 axes
• Injury risk related to DOFs:
  • An injury can occur when motion in a plane exceeds its normal limits, straining soft tissues.
• Planes of motion order and ROM:
  • Sagittal plane typically has the largest ROM, followed by frontal and transverse planes.
  • Sagittal plane motion is usually large; limits in this plane are rarely exceeded in normal activity.
  • Frontal and transverse planes have smaller available ROM, making it easier to exceed limits in those planes.
• Understanding DOFs of each joint is important for assessing movement and injury risk.

Types of Joints

• Three categories:
  • Cartilaginous joints
  • Fibrous joints
  • Synovial joints

Synovial Joints (Type within the three categories)

• Characteristics:
  • No direct union between bone ends.
  • Most common type of joint and most important for physical activity due to wide ROM.
  • Joint cavity filled with synovial fluid; capsule surrounds the joint.
• Joint capsule components:
  • Outer fibrous layer: strong tissue that holds the joint together
  • Inner synovial membrane: secretes synovial fluid
• Articular surfaces: covered with articular cartilage
• Synovial fluid properties:
  • Thixotropic viscosity: dynamic viscosity that varies inversely with joint velocity/rate of shear
  • Viscosity decreases with increased movement velocity, reducing resistance and friction
• Role of anatomy:
  • DOFs and available rotation are largely determined by joint anatomy
  • In many joints, one bone has a convex surface and the other a concave surface; curvature varies between joints
  • Ligaments govern permissible directions and guide motion; together with bone shape determine joint function
• Articular structures: Articular surface, cavity, cartilage, capsule, synovial membrane

Six Types of Synovial Joints

1) Ball and Socket

• Motion occurs actively in all three axes (3 rotational DOFs)
• Example: Hip joint

2) Pivot

• Rotation around one axis (1 rotational DOF)
• Example: Atlantoaxial joint (C1–C2) with dens and atlas/axis alignment

3) Gliding (Plane) joint

• Bones slide past each other; motion tends to be linear rather than angular
• Examples: Midtarsal and Midcarpal joints

4) Hinge

• Articular surfaces molded to permit motion in one plane only

5) Saddle

• Biaxial joint with two opposing surfaces each concave in one direction and convex in the other
• Example: Carpometacarpal joint of the thumb

6) Ellipsoid (Condyloid)

• Similar to ball-and-socket but motion occurs primarily in two directions
• Example: Wrist joint (radius–scaphoid–ulna interactions)

Joints Biomechanics – Factors Influencing Motion at a Joint

• The type and amount of motion and the internal forces required of muscles and ligaments to control the joint depend on:
  1) Joint structure
  2) Interactions Between Joints and the External Environment
  3) External forces applied to the joint

1) Joint structure

• Joint structure described by articular surfaces and ligamentous support.
• Joint surfaces affect amount and type of motion:
  • Congruent surfaces (similar radii of curvature) are more stable.
  • Incongruent surfaces are less stable but allow more motion.
• Radii of curvature describe surface curvature; similar radii → congruent surfaces.
• Curvature and congruence influence the translation-rotation mix during joint motion.
• Joints with relatively flat surfaces allow translation; more curved surfaces allow rotation.
• Clinical example: Knee joint has four articulating surfaces between the femur and tibia, each with a different radius of curvature. These differences enable the combination of rotation and translation during flexion/extension. Clinician needs to understand these complex motions to restore normal motion.

2) Ligamentous support

• Ligaments are designed to provide stabilization without overly restricting motion.
• Synovial joint capsules often have folds that unfold as the capsule stretches to allow more movement.
• Collateral ligaments contribute to stability by limiting side-to-side movement.

3) Interactions Between Joints and the External Environment

• Movement of one joint can affect several nearby joints.
• Example: Standing with the arm at the side, elbow flexion can occur in isolation; but a push-up requires simultaneous wrist and shoulder movements.

4) External Forces on a Joint

• External forces include limb weight and additional loads (e.g., manual resistance, weights).
• These forces apply moments (torques) that rotate the joint.
• Internal forces from muscles and ligaments counteract external moments.
• Static equilibrium exists when external moments balance internal moments; the joint remains at rest or moves at constant speed.
• Identifying external forces helps determine which muscles/ligaments are needed to move or stabilize the joint.
• Joint reaction forces and resulting stresses play a role in joint pain and degeneration; stresses are calculated as ext{stress} = rac{F}{A} where F is the force and A is the contact area.
• External loads influence joint reaction forces; design exercises to minimize joint reaction forces to protect joint surfaces.

Clinical Connections – External Loads and Muscular Demands

• Descending stairs: Gradient moments from head/arms/trunk/opposite leg create a flexion moment at weight-bearing hip and knee.
  • Hip and knee extensors must produce torques to control body weight (eccentric contraction during descent).
• Ascending stairs: Hip and knee extensors must produce concentric torques to lift body weight and extend joints; internal flexion moments from body weight must be overcome.
• Clinical bottom line: Identifying external loads and their effect on joint movement helps determine which muscles contract and the type of contraction needed.

Kinematics

• Kinematics can be broken into two types:
  • Osteokinematics: motions of bones
  • Arthrokinematics: motion at joint surfaces
• Level of analysis dictates which you study:
  • For gross body movement, focus on osteokinematics
  • For injury mechanisms at joints, include arthrokinematics

Osteokinematics

• Motions are described in three planes:
  • Sagittal Plane
  • Frontal Plane
  • Transverse Plane
• Osteokinematic motions in these planes include: Flexion, Extension, Hyperextension, Dorsiflexion, Plantarflexion, Abduction, Adduction, Lateral Flexion, Elevation, Depression, Radial Deviation, Ulnar Deviation, Foot Inversion, Foot Eversion, Internal/Medial Rotation, External/Lateral Rotation, Horizontal Abduction, Horizontal Adduction
• Sagittal Plane Motions:
  • Flexion: Decrease in the angle between two articulating bones
  • Extension: Increase in the joint angle; most joints are in extension in anatomical position
  • Hyperextension: Extension beyond the joint's normal ROM
  • Dorsiflexion: Movement of the foot toward the body; upward (toes toward the shin)
  • Plantarflexion: Movement of the foot away from the body; downward (tiptoe)
• Frontal Plane Motions:
  • Abduction: Distal segment moves away from midline
  • Adduction: Distal segment moves toward midline
  • Lateral Flexion: Side-bending away from midline (often spine)
  • Elevation: Superior movement of the scapula/shoulder girdle
  • Depression: Inferior movement of the scapula/shoulder girdle
  • Radial Deviation: Wrist deviates toward the thumb side
  • Ulnar Deviation: Wrist deviates toward the little finger side
  • Inversion: Inward twisting of the foot
  • Eversion: Outward twisting of the foot
• Transverse Plane Motions:
  • Rotation: Pivoting of a bone on its own axis
  • Internal/Medial Rotation: Rotation toward midline
  • External/Lateral Rotation: Rotation away from midline
  • Hand Pronation: Palm rotates to face downward
  • Hand Supination: Palm rotates to face upward
  • Horizontal Abduction: Shoulder moves away from midline in a horizontal plane
  • Horizontal Adduction: Shoulder moves toward midline in a horizontal plane
• Axes:
  • Sagittal Plane: Mediolateral Axis
  • Frontal Plane: Anteroposterior Axis
  • Transverse Plane: Longitudinal Axis

Combined Motions in Osteokinematics

• Circumduction: A combination of flexion, abduction, extension, and adduction; not a pure planar motion.
• Foot Pronation and Supination: Tri-planar motions that combine flexion/extension, inversion/eversion, and abduction/adduction.
• Pronation: Inward roll of the foot; occurs as the outer edge of the heel strikes the ground and the foot rolls inward and flattens; moderate pronation is necessary for proper function, but excessive pronation can lead to injury.
• Supination: Outward roll of the foot; occurs during heel lift-off as forefoot and toes propel the body forward; excessive supination strains muscles and tendons that stabilize the ankle and can cause ankle sprain or ligament rupture.
• Terminology (pronation vs. supination):
  • Pronation: inward roll of the foot
  • Supination: outward roll of the foot
• Posture implications of osteokinematics: Normal vs abnormal posture relates to internal forces acting as a 'human spring'; abnormal conditions can compress the system and alter force distribution.

Safe and Unsafe Ranges in Pronation/Supination

• Unsafe vs Safe ranges: overpronation, neutral, over-supination
• Visual cues from shoe pedias and stance progression (heel strike to toe-off) help assess pronation status

Open vs Closed Kinetic Chain

• Open Kinetic Chain (OKC): Distal segment is free to move; distal segment moves on proximal segment.
• Closed Kinetic Chain (CKC): Distal segment is fixed to a surface; proximal segments move on the distal segment; motions are more predictable.
• Example relationships:
  • In CKC knee flexion, the ankle typically dorsiflexes and the hip flexes (predictable constraints).
  • In OKC knee flexion, the hip can flex or extend and the ankle can dorsiflex or plantarflex depending on the movement; fewer fixed constraints compared to CKC.

Practical Clinical Insight

• Understanding DOFs, joint structures, and external loads helps clinicians design safer, more effective rehabilitation protocols and exercise programs that minimize harmful joint stresses while enabling functional movement.

References to Key Concepts

• Synovial fluid is thixotropic and becomes less viscous with faster joint movement, reducing friction.
• The congruence of articular surfaces contributes to stability; the knee joint demonstrates a complex multi-surface congruence that enables combined rotation and translation.
• External torques are balanced by muscular/ligamentous internal torques to achieve static or dynamic equilibrium.
• Circumduction and tri-planar foot motions illustrate how complex joint movements can be, even when individual joints move in more than one plane.