Stage 1: The simplistic arm

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 1

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 2 cosine formula

Step 2 cosine triangle

Step 2 defination

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

Step 3 formulaStep 3 defination

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 4 defination

Step 5: Final testing to ensure consistency regardless of position of the third point

Step 5_v1 Step 5_v2 Step 5_v3

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