I want to make a claw that essentially follows a circle for its rotation, where the length of the secants are the same (length of one arm of the claw), and they follow the path of a major arc of a circle that originates from a longer secant, in other words, there are three pieces of information: secant length, number of arms, and longer secant length (we know the coordinates and all), and the radius of the circle is the desired value.
Unfortunately, I have no idea what to do for the math, as I have been thinking about it for hours, and came up with little but a complex addition of sine and cosines:
Horizontal distance:[cos(x) + cos^2(x) - sin^2(x) + cos^3(x) + 3 (-1) cos(x) sin^2(x) + cos^4(x) - 6 sin^2(x) cos^2(x) + sin^4(x)]
Vertical distance:i[ sin(x) + 2 cos(x) sin(x) + 3 cos^2(x) sin(x) + 4 cos^3(x) sin(x) + (-1) sin^3(x) + (-4) cos(x) sin^3(x)].
I considered the idea of simply looking at horizontal distance as the entire thing and pretending vertical distance was 0, this allowed me to get an equation comparing the angle that it would change in terms of r, the ratio of the long secant to the short secant, unfortunately wolfram-alpha solved it for me and got:
Basically, I want to make a robot with 4 arms that are connected at the ends of one another, to be able to have the end of the robot (the claw) reach the specified point, by following an arc as shown in the picture on my original post. This requires math to figure out, but I am at a loss as to what I should do in order to achieve this. I have tried solving for the angle made by each arm of the robot under the conditions that I desire (by essentially adding the effect of each arm), but that has resulted in a complex equation in which I need to solve for the other variable. Unfortunately, asking wolfram-alpha to solve it after I couldn’t do so myself brought no peace (see the second picture with a lot of big parentheses and square roots on it).
Thank you for identifying the field of mathematics that covers things like this. I will look over the Wikipedia article to see if I can figure out the math for my 4-arm robot.
