3MASS OF SEGMENTCalculate 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)
4COM of thigh and footBased 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 isx = ( ) / 2 = 93.0 cmy = ( ) / 2 = 6.15 cmThe thigh center of mass is from the proximal end of the segment. Thus, the center of mass of the thigh isx = ( ) = 78.3 cmy = ( ) cm
5CENTRE OF MASS OF MULTI SEGMENT Xo = (m1x1+ m2x2 + m3x3)/MThe same for Yo.MASS MOMENT OF INERTIAMost 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
6A 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.m2I = Io + mx2 = (0.2)2
7LINK SEGMENT MODELThe process in which the reaction forces and muscle moments are calculated is known as link segment modeling.
8ANATOMICAL 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.
9JOINT REACTION FORCESIn analyzing a segments one at a time, we need to calculate the reaction between segments.
11BONE-ON-BONE FORCESConfusion 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.100100
12FREE BODY DIAGRAM OF A SINGLE SEGMENT Equations:X directionY directionAbout the segment COM
13What 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
14What 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
15Rotation at the top joint (point 1). αTop segment length: aAssume 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.
16CALCULATION 1A 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.