Unified Robotics I: Actuation

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Coordinate Systems

We'll begin by doing a quick review of coordinate systems and coordinate system transforms. Here you can see a position vector designated by the red arrow A in a Cartesian coordinate system. The vector has two components Rx and Ry.

Figure 1 - Vector with two components

It's also possible to express the same vector in polar form. We again need two values two fully specify the vector. In this case we use the magnitude or the length of the vector A, and the angle the vector makes with the X axis (shown here as θ). We can go back and forth between these two different representation s of the vector. The magnitude of the vector can be expressed as the square root of the some of the squares of our Rx and Ry. You've seen that before; it's just the Pythagorean Theorem. The angle θ is given by the arctangent of the ratio of Ry to Rx.

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