Use the table below to calculate the position of the CM of an arm bent at a righ

Question

Use the table below to calculate the position of the CM of an arm bent at a right angle. Assume that the person is 153 cm tall. Take the shoulder to be the origin of coordinates. The arm is held with the upper arm parallel to the floor and the lower arm and hand extended upward. Measure x horizontally from the shoulder to the elbow, and y vertically upward.

Determine the x coordinate of the CM.

Determine the y coordinate of the CM.

TABLE 7-1 Center of Mass of Parts of Typical Human Body, given as % 100 units) (full height and mass Distance of Hinge Hinge Points ) Points from Floor ( %) Center of Mass (x) 1% Height Above Floor) Percent Mass (Joints) Head Trunk and neck 93.5% 91.2% 81.2% 6.9% 46.1% 6.6% Base of skull on spine Shoulder joint elbow 62.2% Hip joint Knee joint Ankle joint Upper arms Lower arms Hands 55.3% 43.1% 4.2% 1.7% wrist 46.2% 52.1% Upper legs (thighs) 42.5% 21.5% 28.5% Lower legs Feet 18.2% 1.8% Body CM = 58.0% 9.6% 3.4% 100.0% 4.0% For arm hanging vertically

Explanation / Answer

Xcm = [Xupperarm * Mupperarm + Xlowerarm*Mlowerarm + Xhand * Mhand] / ( Mupper arm + Mlower arm + Mhand)

Xcm = [(81.2 - 71.7)(6.6) + (81.2-61.2)*(4.2+1.7)]/( 6.6 + 4.2 + 1.7) = 14

Ycm =  [Yupperarm * Mupperarm + Ylowerarm*Mlowerarm + Yhand * Mhand] / ( Mupper arm + Mlower arm + Mhand)

Ycm = [ 0 + (62.2 - 55.3 ) ( 4.2) + (62.2 - 43.1)(1.7) / ( 6.6 + 4.2 + 1.7) = 4.92

Xcm = 14% of 153 = 21.42 cm

Ycm = 4.92 % of 153 =7.53 cm

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