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• Joint Biomechanics Definitions
  • Joint reaction force defined as force generated within a joint in response to forces acting on the joint
    • in the hip, it is the result of the need to balance the moment arms of the body weight and abductor tension
    • maintains a level pelvis
  • Coupled forces
    • when two movements and associated forces are coupled
  • Joint congruence
    • relates to fit of two articular surfaces
    • high congruence increases joint contact area
  • Instant center of rotation
    • point about which a joint rotates
    • often changes during rotation due to joint translation
    • center of gravity of human is just anterior to S2
  • Friction and lubrication
    • not a function of contact area
    • lubrication decreases friction
    • examples
      • coefficient of friction of human joints is .002 to .04
      • TJA (metal on PE) is .05 to .15

• Free Body Analysis Definitions
  • Newtons laws
    • first law
      • if there is no net force on an object, its velocity remains constant
    • second law
      • force equals mass multiplied by acceleration
      • F=ma
    • third law
      • when a first body exerts a force on a second body, the second body exerts a force that is equal in magnitude and opposite in direction on the first body
      • F2=-F1
  • Force
    • definition
      • a push or pull on an object resulting from the object's interaction with another object
    • equation
      • force = mass x acceleration, F=ma
      • 1 Newton = force required to give 1 kg mass an acceleration of 1 m/s2
  • Vector
    • definition
      • a quantity that contains both direction and magnitude
      • scalar quantities do not have direction
    • forces and velocity can be broken down into vectors
  • Moment (torque)
    • definition
      • the tendency of a force to rotate a body around an axis
    • equation
      • moment (torque) = force(perpendicular) X distance
  • Work
    • definition
      • when a force acts upon an object to create displacement
    • equation
      • work = force (vector parallel to displacement) x distance
  • Energy
    • definition
      • ability of an object to perform work
    • classification
      • potential energy
        • equation
          • U (potential energy) = mass x gravity x height
      • kinetic energy
        • equation
          • KE (kinetic energy) = 1/2mv2

• Hip Free Body Analysis
  • Free body analysis diagram
    • W = gravitational force
      • weight of the body minus weight of ipsilateral extremity (or 5/6 body weight)
    • M = abductor muscle force
    • R = joint reaction force
      • can reach 3 to 6 times body weight
  • Solving for joint reaction force (R)
    • step 1: calculate My
      • principle
        • the sum of all moments must be zero
        • in this case, the moments are created by My (abductor moment) and W (bodyweight moment)
      • equation
      • (A x My) = (B x W)
        • assume A = 5cm and B = 12.5cm (this information will be given to you)
        • My = 2.5W
    • step 2: calculate Ry (vertical component of joint reactive force)
      • Ry = My + W
      • Ry = 2.5W + W
      • Ry = 3.5W
    • step 3: calculate R (total joint reactive force)
      • R = Ry / (cos 30°)
        • R = 3.5W / (cos 30°)
        • R = ~4W

• Clinical Implications
  • Actions that decrease joint reaction force include
    • increase in ratio of A/B (shift center of rotation medially)
      • acetabular side
        • moving acetabular component medial, inferior, and anterior
      • femoral side
        • increasing offset of femoral component
        • long stem prosthesis
        • lateralization of greater trochanter
          • by using increased offset neck/prosthesis
        • varus neck-shaft angulation
          • increases shear across joint
      • patient's gait
        • shifting body weight over affected hip
          • this results in Trendelenburg gait
        • cane in contralateral hand
          • reduces abductor muscle pull and decreases the moment arm between the center of gravity and the femoral head
        • carrying load in ipsilateral hand
          • produces additional downward moment on same side of rotational point
  • Actions that increase joint reaction force include
    • valgus neck-shaft angulation
      • decreases shear across joint