The conceptual and closed-form dimensional synthesis of a high-accuracy four-position tilt mechanism is discussed in detail. The mechanism, which consists of a customized five-bar linkage, is capable of accurately rotating an optical bench, which supports an object such as a space instrument, or another type of similar platform to four required and discrete angular postures. The mechanism is driven by two stepper motors. Due to the special characteristics of the five-bar linkage, even relatively large stepper motor errors produce very minor errors in the four desired angular postures of the optical bench. The dimensional synthesis of the mechanism involves solving a system of four non-linear equations in four unknowns. A methodology is introduced for reducing this system of non-linear equations to a closed-form quadratic equation in one unknown. A numerical example of the closed-form dimensional synthesis methodology is also presented.
On pure bending in non-linear elasticity: A circular closed-form 2D solution for semi-linear orthotropic material