Unloading a painful hip can often be accomplished with a can

Unloading a painful hip can often be accomplished with a cane. Using the illustration below, is there a difference if one uses the cane on one side or the other? The distances are in cm. and the pain is on the left side.

Solution

Let CF = cane force which acts vertically upwards

By geometry, Distance between F_JB and F_AB = (40 - 30)/ sqrt2 = 10 / sqrt2 cm

With no cane:

Balancing moments about the point of application of F_JB force,

F_AB * (10 / sqrt2) + BW*30 = 0

F_AB * (10 / sqrt2) + BW*30 = 0

F_AB = -BW*3*sqrt2

When cane is on left side:

Balancing forces in horizontal direction, F_AB * cos45 + F_JB * cos45 = 0

F_AB = - F_JB

Balancing forces in vertical direction,

CF + F_AB * sin45 + F_JB * sin45 = BW

CF = BW

Balancing moments about the point of application of F_JB force,

F_AB * (10 / sqrt2) + BW*30 + CF*(60 - 30) = 0

F_AB * (10 / sqrt2) + BW*30 + BW*30 = 0

F_AB = -BW*6*sqrt2

When cane is on right side:

Balancing forces in horizontal direction, F_AB * cos45 + F_JB * cos45 = 0

F_AB = - F_JB

Balancing forces in vertical direction,

CF + F_AB * sin45 + F_JB * sin45 = BW

CF = BW

Balancing moments about the point of application of F_JB force,

F_AB * (10 / sqrt2) + BW*30 - CF*(60 + 30) = 0

F_AB * (10 / sqrt2) + BW*30 - BW*90 = 0

F_AB = BW*6*sqrt2

Clearly the cane takes more load when on right side than on left.