ANTROPOMETRIC DATA Segment Dimensions – Body segment lengths can be expressed as a fraction of body height, H.

ANTROPOMETRIC DATA

MASS OF SEGMENT Calculate COM of thigh and foot using antropometric data. Coordinates: Ankle (84.9, 11.0), metatarsal (101.1,1.3), greater trocanter (72.1, 92.8), lateral femoral condyle (86.4, 54.9)

COM of thigh and foot Based on table 3.1, foot COM is 0.5 of the distance from the lateral malleolus (ankle to the metatarsal marker. Thus, the center of mass of the foot is x = (84.9 + 101.1) / 2 = 93.0 cm y = (11.0 + 1.3) / 2 = 6.15 cm The thigh center of mass is 0.433 from the proximal end of the segment. Thus, the center of mass of the thigh is x = 72.1 + 0.433 (86.4 - 72.1) = 78.3 cm y = 92.8 - 0.433 (92.8 - 54.9) - 76.4 cm

CENTRE OF MASS OF MULTI SEGMENT Xo = (m1x1+ m2x2 + m3x3)/M The same for Yo. MASS MOMENT OF INERTIA Most body segment do not rotate about their mass center, but rather the joint at either end. The parallel axis theorem is used to calculate the moment of inertia in such cases. I = Io + mx2

A Prosthetic leg has a mass of 3 kg and a center of mass of 20 cm from the knee joint. The radius of gyration is 14.1 cm. Calculate I about the knee. Io = 3(0.141)2 kg.m2 I = Io + mx2 = 0.06 + 3 (0.2)2

LINK SEGMENT MODEL The process in which the reaction forces and muscle moments are calculated is known as link segment modeling.

ANATOMICAL VS LINK SEGMENT MODEL. Joints are replaced by hinge joints and segments are replaced by masses and moments of inertia located at each segment’s centre of mass. It represents all the forces acting on the total body system itself.

JOINT REACTION FORCES In analyzing a segments one at a time, we need to calculate the reaction between segments.

FBD

BONE-ON-BONE FORCES Confusion between joint reaction and bone –on-bone forces. Bone-on-bone forces: actual forces acting on the articulating surfaces and include the effect of muscle activity. 100 100

FREE BODY DIAGRAM OF A SINGLE SEGMENT Equations: X direction Y direction About the segment COM

What are the forces acting in X directions (linear movement) in the single segment in previous slide? We can assume that Rx1, Rx2 are acting in the x direction and right direction is positive. Therefore the equation is Rx1-Rx2=max If everything is in static condition (standing without movement for example, then Rx1-Rx2=max=0 or Rx1=Rx2

What are the forces acting in Y directions (linear movement) in the single segment in previous slide? We can assume that Ry1, Ry2 and weight are acting in the y direction and upward direction is positive. Therefore the equation is, Ry1-Ry2-m1g=may If everything is in static condition (standing without movement), then Ry1-Ry2-m1g=may=0

Rotation at the top joint (point 1). α Top segment length: a Assume that the length of the segment is a and this segment is tilting at angle α from vertical. ΣM=I1ω M1-M2 - Rx2.a sin α - Ry2 cos α - m1g (a/2) cos α = I1 ω In static condition, the above equation is equal to 0. M1-M2 - Rx2.a sin α - Ry2 cos α - m1g (a/2) cos α = 0.

CALCULATION 1 A person standing on one foot on a force plate. The GRF is found to act 4cm anterior to the ankle joint. The COM is 6 cm measured horizontally from the ankle joint. The subject mass is 60 kg and the mass of the foot is 0.9kg. Draw a free body Diagram of the foot. Calculate the joint reaction forces and net muscle moment at ankle.