From the figure below what is the angle of the thigh segment

From the figure below, what is the angle of the thigh segment? We know the X and Y coordinates of the following segments: hip (2.128,1.891), knee (2.122,1.642), ankle (1.897,1.210).. Calculate the relative angle at the knee and the absolute angles of the thigh and leg segment.

Solution

As per the values given

Hip = 1.5,10

Knee = 6,6

Ankle = 2,2

The angle of the thigh will be the angle between

Hip-Knee and Knee-ankle vector

Hip-Knee = ( 1.5 -6 ) i + (10- 6) j = -4.5 i + 4 j

Ankle Knee = ( 2 -6 ) i + ( 2 - 6) j = -4 i - 4 j

we know that the angle between two vectors is given by

Theta = cos^-1 (A.B)/AB

Theta = cos^-1 (-4.5 i + 4 j . -4 i - 4 j )/ 6 *5.65 = 86.61 degree