Modelling the arms was challenging to turn into 2 dimensional motion. For the purposes of this analysis I said that the arms were a 5 linkage system with a slider crank as shown in the diagram below. I did the analysis based off of this diagram and measurements I took while building it. I said that the angle between L4 and L5 (the upper arm and the forearm) was 90 degrees and the input crank moved with w2 = 10 deg/s and a2 = 0 deg/s^2. I also used the position, velocity and acceleration of L3 that I calculated in the first section finding the position of the head.
First, the position of the arms is shown in the following graph. I looked at the vertical position of the forearm arms in the same plane as the head and it’s angle. The arms move in the opposite direction of the head, i.e. when the head goes up the arms lower to reveal the head and when the head drops back down the arms go up to hide the face.
Next I looked at the linear velocity of the arms by taking the derivative of the positional loop. For the purposes of this graph y is defined as up and down along the motion of the head and x is defined as the forward motion towards and away from the nose. I also calculated the linear and angular acceleration of the forearms
