Screw Theory

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Chapter 4 Screw Theory

In this chapter, we take a pause from our study of rigid body kinematics to introduce a mathematical object called screw. Screws form a special class of vector fields which satisfy the relationship \(\vel_Q=\vel_P + \bV \times \br_{PQ}\text{,}\) where \(P\) and \(Q\) are any two points of space \(\cE\) (whether \(\cE\) is in motion or not is irrelevant here). They will be used throughout this book to provide a simple formalism which unifies all aspects of rigid body mechanics. We have seen in Chapter 3 that the velocity field of a rigid body \(\cB\) defines a screw. However, other relevant vector fields share this characteristic. Historically, they find their origin in the work of Chasles (in kinematics) and Poinsot¹(for systems of forces). The concept of screws was defined by astronomer Ball², but is also present in the work of Plücker, Klein, and von Mises. The definition and notations adopted here were first proposed by Glaymann³.