Well, as it turns out, dapontes made one 4 years ago. ._. a = the arm length r = radius of circle t = turning velocity Click to re-position the circle at the mouse.
Entry for the Mathematica Competition Round 1, Division Gamma. All my calculations were done with pen and paper. Θ = angle of the wheel. Φ = angle opposite of the radius. φ = angle between the radius and arm. How it works: 1. Find the difference in the y from the circle's y to a point using h = r * sin(Θ - 90) 2. Use the trig ratio sinΦ = (h / a) to find the second angle Φ with Φ = asin(h / a). 3. Because the angles add up to 180 in a triangle, find the third angle φ with φ = 180 - (Φ + Θ). 4. Use the Law of Sine (but in Scratch, sine is switched with cosine) to find the difference in x from the center to the arm end, using (-cosΘ / a) = (cosφ / b) which turns into b = (a * cosφ) / -cosΘ So then the x position of the arm end would be the circle's x + b, if, and only if Θ does not = 90 or 270. Otherwise, b = a ± r. Note: The arm length can't be less than the diameter (r*2) of the circle. You may use this for your projects if you give credit.
