ARTICULATED ARMS
In robotics, it is important to have control over articulated mechanisms. What is the reach of the “arms” of a certain robot? The space of possible positions of these mechanisms is often intricate.
In the mechanism we present below, we use colors to understand the reach of each arm. If it were not connected to the others, each arm would allow positioning the red dot along a circular ring, which is represented on the board by one of the primary colors red, green or blue.
In the positions allowed to the 3 arms simultaneously the color is white (the mixture of the 3 colors in equal proportions). In positions where none reaches, the color is black. And in those where only two can, it is the mixing (by addition) of the two corresponding colors. Therefore, the white region, which is a kind of hexagon with circular edges, is the set of points accessible to the mechanism.
