![]() Here, D1 can be calculated in two ways: The arcsine of y/dist or the arctangent of y/x. In the following diagram, x, y, and dist define a right-angled triangle. ![]() This comes handy in two places, as we’ll see shortly.įrom the robotic arm diagram above (the one with D1, D2, dist, etc), we can directly derive the first formula: A1 = D1 + D2ĭ1 is fairly easy to calculate. With this version, we can calculate angle C from the triangle’s sides a, b, and c. We do not need the basic form, but rather the transformed version that you can see below the original formula. The law of cosines (see the first formula in the figure above) is a generalization of the Pythagorean theorem (c 2 = a 2 + b 2 for right(-angled) triangles) to arbitrary triangles. Now is a good moment to dig out an old trig formula you may remember from school: The law of cosines. Furthermore, dist divides angle A1 into two angles D1 and D2. It points from (0,0) to (x,y), and as you can easily see, the three lines dist, len1, and len2 define a triangle. In the diagram you also see a new dotted line named dist. The tip of segment 2 points to (x,y), and we want to calculate back from that point to the yet unknown values of A1 and A2.The second joint describes an angle A2 measured from the first segment (counterclockwise in both cases).The root joint describes an angle A1 measured from the x axis.The segments have the length len1 and len2, respectively. ![]() This diagram tells us a couple of things: Let me just tweak the diagram a little by replacing some of the labels and adding one line and two angles: Here is a schematic diagram of our robot:Īpplying the geometric approach to the SCARA robot Now you know why our robot just serves tea.) (Robot hands would have additional degrees of freedom, and remember that we want to keep things simple.
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