![]() Let’s say that you have a vector a which describes a point in our Cartesian space, and you’d like move it a little bit up to describe a point that is 5 units higher on the z-axis. Vectors are usually denoted by lowercase, bold letters like a or lowercase letters with an arrow on top. In the image above, the a arrow represents a vector, where the a x line represents the x-coordinate for the vector (and similarly for a y and a z). You’re now at the point that the vector describes!Īgain, a vector like this represents a point in our Cartesian space, and is usually visualized as an arrow or line: Now walk 7 units up the y-axis, then stop again.Imagine you are standing at the origin.You can visualize the location of this (or any) point by using this simple technique: The number at index 1 is the first number, the number at index 2 is the second number, and so on. We call the position of a number in a vector the index to help identify which number in a vector we are talking about. In the case of the vector above, this point is 5 units past the origin on the x-axis, 7 units past the origin along the y-axis, and 9 units past the origin on the z-axis. The top number represents the x-coordinate, the second the y-coordinate, and the bottom number is the z-coordinate. A vector is just a one-dimensional array of these three coordinates, and looks like this: ![]() To make things nice and compact, we’ve developed a handy notation for describing these three coordinates in a Cartesian coordinate system, called vectors. How far north or south it is from the origin.How far east or west it is from the origin.How far up or down it is from the origin.Given these things, we can identify any point in space by just 3 numbers: The origin is the place in the image labeled O where these three axis’ intersect, which is right in the middle of the space. The y-axis runs east-west, and the x-axis runs north-south. The z-axis is the line that runs up-down. The axis’ (pronounced “axe-ees”) are the three lines labeled X, Y and Z that you see in the image above. In a Cartesian coordinate system, there two very important things to understand: The origin and the axis’. It’s just a tool! The Origin and the Axis’ There are lots of other kinds of mathematical spaces that are used to describe real-space, but Cartesian space is the easiest for our purposes here. the space that you are living in right now) in a more specific and workable way. It’s just a mathematical model to help us describe real space (i.e. ![]() There is nothing special about Cartesian space. Welcome to Cartesian coordinate space! We’ll be spending a lot of time here, and because it’s so important to building, developing and programming robotic arms, we’ll need to get comfortable working with it to describe how things exist and move (specifically, chains of rigid bodies) within it.
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