Hi, We were tasked by improving Theo jansen walking mechanism. We brainstormed offered our improvement and all got rejected by our instructor. It got to the point where we have no Idea how and what and why and where should we do. I guess y'all can sense the frustration at the moment lol. anyways So my last thought was to keep the mechanism as is and add differential concept into it to allow the robot to rotate left and right. I doubt this would get approved but i would appreciate if y'all have any idea on how to guide us towards what you think might be appropriately approved..Whatever the design is we have to also provide it's Kinematics calculations and so on.
I think we'd have to know more about the nature of your class, and possibly about your instructor's tastes to guide you here. Spitballing, what the mechanism does is translate a rotational motion to an offset linear motion, and then a non-linear return motion that does not cross over the line of the linear motion - thus 'walking'. It's a rather elegant mechanism, taking into account the artistry of its form, so improving it is quite non-trivial. There are a number of linkages or mechanisms that translate rotation to linear motion. You might start there.
Something relatively basic - but the kind of thing a university prof might be looking for - is realizing that the triangular sections form essentially fixed structures. Each of the two triangles can be replaced by a single piece that hinges at two/three points