Robotics calculating degree of freedom example
Now, let’s apply the cosine rule to the particular triangle we looked at a moment ago. It’s a bit like Pythagoras’ theorem except for this extra term on the end with the cos a in it. So, the cosine rule is simply this relationship here. So, all together, the sides are labelled capitals A, B and C, and the angles are labelled little a, little b, and little c. And, we do the same for this edge and this angle, and this edge and this angle. We don’t have to have any right angles in it and we’re going to label the length of this edge as A and the angle opposite that edge, we’re going to label as little a. And, if you’re a little rusty on the cosine rule, here is a bit of a refresher. In order to do that, we need to use the cosine rule.
![robotics calculating degree of freedom example robotics calculating degree of freedom example](http://1.bp.blogspot.com/-mg-MbrW3UV0/VbjChJ7e7KI/AAAAAAAAAe4/RJx0uVCUlRQ/s320/degree-of-freedom-slider-cr.png)
Now, we’re going to look at this triangle highlighted here in red and we want to determine the angle alpha. And, using Pythagoras theorem, we can write r squared equals x squared plus y squared. We know that the end point coordinate is x, y, so the vertical height of the triangle is y, the horizontal width is x. We’re going to overlay the red triangle on top of our robot.
![robotics calculating degree of freedom example robotics calculating degree of freedom example](https://media.cheggcdn.com/study/c1c/c1ca55c5-c652-40b9-9f73-67961c0d0346/image.png)
We’re going to start with a simple piece of construction. The solution that we’re going to follow in this particular section is a geometric one.
![robotics calculating degree of freedom example robotics calculating degree of freedom example](http://2.bp.blogspot.com/-pZH9MJkp-JE/VbjGrTreXfI/AAAAAAAAAfQ/XIgLOLdXMSY/s1600/degrees-of-freedom-structur.png)
So, the problem here is that given x and y, we want to determine the joined angles, Q1 and Q2. The tooltip pose of this robot is described simply by two numbers, the coordinates x and y with respect to the world coordinate frame. We saw this simple two-link robot in the previous lecture about forward kinematics.