Screw Mechanics

This book starts from the general concepts of force and torque and deduces the force screw naturally. The displacement, velocity, and acceleration of a rigid body and rigid-body system are discussed in geometry and algebra with a focus on increasing the intuitive understanding of the readers. Velocity screw is explained in vector geometry. Momentum screw of a rigid body and the theorem of momentum and moment of momentum are investigated for deducing the dynamics of a rigid body and rigid-body systems. This is the first time to interpret momentum and moment of momentum in such a way. All profound theories are explained in simple language. Screw mechanics focuses on the screw expression of mechanics from statics, to kinematics and dynamics of a rigid body and rigid-body systems. Therefore, the general scope of the book’s content covers from the definition of force screw to the deduction of the screw equation of statics in Newton’s first law, the investigation of the kinematic geometry of rigid-body motion, the deduction of the velocity screw of the end effector in a series kinematic chain from algebra and geometry. The kinetostatics is discussed for force control of a robotic arm. Acceleration in screw form is deduced for establishing the dynamics in Newton-Euler equations. Theorem of kinetic energy expressed in screw is discussed from the viewpoint of deducing the Lagrangian dynamics. Comparison of dynamics in momentum screw, kinetic energy and Newton–Euler equations is commented objectively at last. Screw Mechanics introduces a revolutionary way to map the force, velocity and momentum of a rigid body or system from 3-dimensional space to force screw, velocity screw and momentum screw of one single point in 6-dimensional space of screw. By adopting screw theory as a foundational language, this book presents a unified and elegant framework that seamlessly integrates statics, kinematics, and dynamics. The content starts from a primary level and comes to a very high level. Therefore, the intended readership includes undergraduate students and postgraduate students and scholars in mechanics, robotics, aerospace engineering, civil engineering, mechanical engineering, and vehicle engineering.