M.Sc Thesis
M.Sc Student Chakon Ofir Theoretical and Experimental Investigation of Twistcar Movement Dynamics Department of Mechanical Engineering Professor Yizhar Or

Abstract

Mobile robotic systems may contain several bodies which are connected to each other with joints and compose a kinematic chain. Kinematic relations between the bodies are typically expressed by constraints. A constraint which limits the relative motion between two bodies in a system is called holonomic. Holonomic constraints reduce the effective number of the system’s degrees of freedom. On the contrary, non-holonomic constraints do not reduce the system’s degrees of freedom; instead, they reduce the dimension of the space of instantaneous velocities. Many studies investigated mechanical systems with non-holonomic constraints and they mainly discuss aspects of controllability and gaits generation by utilizing methods of geometric mechanics and non-linear control.

In this study we investigate the dynamic behavior of the Twistcar and Roller-Racer vehicles in order to demonstrate how a simple children’s toy can leave a trail of non-intuitive questions behind it. Twistcar and Roller-Racer are plastic ride-on toy cars which consist of two axles: the main axle and the steering wheel axle. They are propelled by applying oscillations of the steering wheel angle about a nominal value. Their dynamics are governed by a combination of momentum balance and non-holonomic constraints of no-slip at the wheels’ axles. The only difference between Twistcar and Roller-Racer is that the nominal relative angle between the steering wheel link and the main link is  in the Roller-Racer, rather than  in the Twistcar.

Roller-Racer has been extensively investigated in previous studies under periodic steering wheel angle input using two assumptions which are physically questionable:

1)      The mass of the steering wheel link is zero, while its moment of inertia is nonzero.

2)      The main link’s center of mass is located above the back axle which practically may result in tendency of the vehicle to tip over.

Additionally, they assume that the rider directly prescribes the steering wheel angle as a controlled input, and do not consider the possibility that the true mechanical input might be the torque at the steering wheel axle.

The goal of our study is to analytically investigate the dynamics of the Twistcar and Roller-Racer vehicles, without using the two assumptions above, under periodic excitation of steering wheel angle or torque input. Our focus is on formulation without using geometric mechanics terminology, but rather using vector calculus and algebraic terminology. Approximate expressions for the influence of the vehicle parameters on the motion are derived by utilizing method of perturbation expansion.