SAQMG2

Linked segment models are made up of body segments.

Two main assumptions usually adopted for a link segment model are that the body segments are rigid and the joints are frictionless.

In inverse dynamics the motion is measured and the resultant force iscalculated.

The three types of forces that act on a body segment are external, internal and inertial.

It is justifiable to treat a link segment model as quasi-static only when theaccelerations are small.

The results of this SAQ are dependent on your own dimensions. As an exampleI will use the following dimensions, height = 193 cm, measured upper limblength = 75 cm, and measured lower limb length = 100 cm.Length of upper limb is calculated as follows using the ratios given in Figure 9:LUPPER = (0.186 + 0.146 + 0.108) H = 0.440 × 193 = 85 cmLength of lower limb is calculated as follows:LLOWER = (0.186 + 0.146 + 0.108) H = 0.530 × 193 = 102 cmIf the calculated limb lengths are compared to measured limb lengths it can be seen that the calculated lower limb lengths are reasonable estimates. However, the calculated upper limb length is 10 cm out. This illustrates the diversity of human dimensions and why standardised data sets should only be used when actual measurements are not available.

To calculate the mass of the thigh, mTHIGH, the ratio reported in Table 1 is used:mTHIGH = 0.100mBODY = 0.100 × 80 = 8.0 kgTo calculate the position of the centre of mass of the thigh relative to itsproximal end, IPROXIMAL, the ratio, 0.433, reported in Table 2 is used:IPROXIMAL = 0.433ITHIGH = 0.433 × 390 = 169 mmTo calculate the position of the centre of mass of the thigh relative to itsproximal end, IDISTAL, the ratio, 0.567, reported in Table 2 is used: IDISTAL = 0.567ITHIGH = 0.567 × 390 = 221 mmThe mass of the thigh is 8.0 kg, and its centre of mass is located 169 mm distal to the greater trochanter and 221 mm proximal to the femoral condyles.Note that the centre of mass is closer to the proximal end than to the distal end. This is mainly due to the shape of the thigh which narrows towards its distal end so that more mass is distributed towards the proximal end. The position of the centre of mass is also dependent on the densities of the various tissues, such as bone, muscle and fat, and how they are distributed.

Calculating the mass of the lower leg and foot complex, m, using the ratio,0.061, in Table 1:m = 0.061 × 75 = 4.575 kgCalculating the radius of gyration about the centre of mass, kCM, using the ratio 0.416, given in Table 2:kCM = 0.416L = 0.416 × 450 × 10-3 = 0.1872 = 0.19 mCalculating the moment of inertia about the centre of mass, ICM:ICM = mAkCM = 4.575 × 0.1872 × 0.1872 = 0.1603 = 0.16 kg m2Calculating the radius of gyration, kP, using the ratio 0.735, and moment ofinertia, IP, about the proximal end:kP = 0.735L = 0.735 × 450 × 10-3 = 0.33075 = 0.33 mIP = mkP = 4.575 × 0.33075 × 0.33075 = 0.50048 = 0.50 kg m2Calculating the radius of gyration, kD, using the ratio 0.572, and moment ofinertia, ID, about the distal end:kD = 0.572 × L = 0.572 × 450 × 10-3 = 0.2574 = 0.26 mID = mkD = 4.575 × 0.2574 × 0.2574 = 0.3031 = 0.30 kg m2The radius of gyration about the proximal end is larger than the radius ofgyration about the distal end because more mass is distributed further from the proximal end than the distal end.