This paper investigates methods for steering systems with nonholonomic constraints between arbitrary configurations. Brockett's work on optimal controls for canonical systems is used as motivation to derive suboptimal trajectories for non-canonical systems, where multiple levels of Lie brackets are needed for controllability. These trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. A class of systems, called chained systems, can be steered using sinusoids, and conditions are given for converting two-input systems into this form. Nonholonomic constraints arise from the nature of the controls or conservation laws. Examples include mobile robots, multifingered hands, and space robotics. These constraints restrict the system's motion and require specialized motion planning algorithms. The paper discusses the use of sinusoidal inputs for steering systems, particularly for first-order and second-order systems. For first-order systems, sinusoids at integrally related frequencies are used to steer the system between configurations. For second-order systems, multiple cycles of sinusoidal inputs are used to achieve motion in desired directions. The paper also introduces chained systems, a simpler class of nonholonomic systems that can be steered using sinusoids. These systems have a specific structure that allows for efficient steering. The paper provides examples of chained systems and shows how they can be transformed into chained form. The use of sinusoids for steering nonholonomic systems is shown to be effective for certain classes of systems, particularly those with maximum growth. The paper concludes that while steering nonholonomic systems using sinusoids is challenging, it is possible for certain classes of systems, and the approach provides a useful framework for motion planning.This paper investigates methods for steering systems with nonholonomic constraints between arbitrary configurations. Brockett's work on optimal controls for canonical systems is used as motivation to derive suboptimal trajectories for non-canonical systems, where multiple levels of Lie brackets are needed for controllability. These trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. A class of systems, called chained systems, can be steered using sinusoids, and conditions are given for converting two-input systems into this form. Nonholonomic constraints arise from the nature of the controls or conservation laws. Examples include mobile robots, multifingered hands, and space robotics. These constraints restrict the system's motion and require specialized motion planning algorithms. The paper discusses the use of sinusoidal inputs for steering systems, particularly for first-order and second-order systems. For first-order systems, sinusoids at integrally related frequencies are used to steer the system between configurations. For second-order systems, multiple cycles of sinusoidal inputs are used to achieve motion in desired directions. The paper also introduces chained systems, a simpler class of nonholonomic systems that can be steered using sinusoids. These systems have a specific structure that allows for efficient steering. The paper provides examples of chained systems and shows how they can be transformed into chained form. The use of sinusoids for steering nonholonomic systems is shown to be effective for certain classes of systems, particularly those with maximum growth. The paper concludes that while steering nonholonomic systems using sinusoids is challenging, it is possible for certain classes of systems, and the approach provides a useful framework for motion planning.