The human limbs follow a kind of the same angular motion. If we were to look at the shadows of our arms and legs, we would not be able to differentiate them if they were presented in the same orientation and the end parts, finger or feet, were covered by a rectangular box.
The arm is made up of 2 link and 3 joints (shoulder, elbow and wrist). This can be represented in grasshopper as points (joints) and lines (link). We shall just assume that each link as only 1 muscle to keep the design simple.
Step 1: Create a point in Rhinoceros3D and link it the its grasshopper plugin
Step 2: Fix the first joint and calculate the location of the second joint
The 1st joint is at the origin and the other joint is at a point which will be calculated using the law of cosine shown below
Step 3: Ensure that the lines are of uniform length even though the third point can be positioned anywhere in the 3d space
After finding the angle found within the triangle, I had to find the angle between the shoulder-elbow link and the horizontal axis by using formula to find angles of a right-angle triangle
Once, the angle found found, I fixed the hypotenuses (shoulder-elbow link) to a constant and then calculate the new X,Y coordinates of the elbow
In addition, I also took care of the situation then the movable point (hand) is on either side of the elbow since this determined whether to add or subtract the length calculated from the elbow’s coordinates
Step 4: Add simplistic muscle and fingers
Step 5: Final testing to ensure consistency regardless of position of the third point