Mathematics of the Slider Cranks
1. Generic Slider Crank
This is the generic slider crank (C02):
In this picture a crank CA is constrained to rotate around the point C. Link AB is the connecting rod and B is the slider that slides along CE. We have fixed lengths AC = a and AB = b. The length CB = x varies as the crank is moved. When CA is rotating around C we can describe its position with respect to the angle ACB = that we measure from CB counterclockwise from CB to CA. How can we determine the length of CB, when the crank is moving (that is, when AC is being rotated around C)?
Let us use some geometry and basic trigonometry here. Let us construct AD perpendicular to CB; then, from the right triangle ACD, we can determine
Note that when > 90° then D is to the right of C and CD is negative and when > 180° then A is above CE and AD is negative.
Also, notice that
By the Pythagorean Theorem,
2. Inversions of the Slider Crank (C02, C05, D2)
3. Offset Slider Cranks (D01, C04)
4. Topological Extensions of the Slider Crank (D14, D07, D08, C06)