I'm looking to understand the rotational dynamics of a joint in relation to the actual servo angle, as depicted by the four-link mechanism in the attached image.
The lengths of r1, r2, r3, and r4 are fixed, with θ1 representing the servo angle. My goal is to determine θ2, which will allow me to apply it to a set of inverse/forward kinematic equations.
Here's the robotic arm in question:
Due to the differing lengths of r2 and r4 in the arm, I'm uncertain about how to establish the correlation between θ1 and θ2. I would be very thankful for any guidance on this matter.
Calculating θ1 given the values of r1, r2, r3, r4, and θ2 is straightforward. However, the relationship between θ1 and θ2 isn't straightforward—it's not linear. My initial attempt to use a simple proportional relationship, like θ1 = K * θ2 with K being a constant, was inadequate. I've discovered that it's a type of 4-bar linkage, which is governed by the Freudenstein equations listed below. To be frank, solving the system of equations for either angle is turning out to be more complex than I anticipated for a robotic kit designed for educational purposes. We're utilizing PictoBlocks and CodeSkool to develop the scratch sketch, but unfortunately, there's no available scratch extension for this type of robotic arm.
