Introduction

Underactuated mechanical systems refer to those mechanical systems which have more degree of freedom than the number of actuators. Most of the underactuated mechanical systems are suffered from nonholonomic constraints. The reasons of "underactuation" are mainly due to the following reasons: kinematics or dynamics of the system are inherently underactuated; part of the actuators are removed for reducing cost or other practical purposes; actuator failure; artificially creating a complex low-order nonlinear system to obtain insight into high-order underactuated systems. In classical mechanical systems, nonholonomic constraints can be divided into two classes, the first order nonholonomic constraints and the second order nonholonomic constraints. For the first order nonholonomic constraints, the constraints are defined on the coordinates and velocities of the mechanical systems, whereas for the second order nonholonomic constraints, the constraints involve accelerations of the mechanical systems. This chapter provides an example for both first-order nonholonomic constraint and second order nonholonomic constraints.