|
Twist (screw Theory)
Screw theory is the algebraic calculation of pairs of vectors, such as forces and moments or angular and linear velocity, that arise in the kinematics and dynamics of rigid bodies. The mathematical framework was developed by Sir Robert Stawell Ball in 1876 for application in kinematics and statics of mechanisms (rigid body mechanics). Screw theory provides a mathematical formulation for the geometry of lines which is central to rigid body dynamics, where lines form the screw axes of spatial movement and the lines of action of forces. The pair of vectors that form the Plücker coordinates of a line define a unit screw, and general screws are obtained by multiplication by a pair of real numbers and addition of vectors. An important result of screw theory is that geometric calculations for points using vectors have parallel geometric calculations for lines obtained by replacing vectors with screws. This is termed the ''transfer principle.'' Screw theory has become an im ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Stawell Ball
Sir Robert Stawell Ball (1 July 1840 – 25 November 1913) was an Irish astronomer who founded the screw theory. He was Royal Astronomer of Ireland at Dunsink Observatory. Life He was the son of naturalist Robert Ball, and Amelia Gresley Hellicar. He was born in Dublin. and was educated at Trinity College Dublin where he won a scholarship in 1859 and was a senior moderator in both ''mathematics'' and ''experimental and natural science'' in 1861. Ball worked for Lord Rosse from 1865 to 1867. In 1867, he became Professor of Applied Mathematics at the Royal College of Science in Dublin. There he lectured on mechanics and published an elementary account of the science. In 1873, he became a Fellow of the Royal Society. In 1874, he was appointed Royal Astronomer of Ireland and Andrews Professor of Astronomy in the University of Dublin at Dunsink Observatory. Ball contributed to the science of kinematics by delineating the screw displacement: :When Ball and the screw theorists spe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Number
In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every real number can be almost uniquely represented by an infinite decimal expansion. The real numbers are fundamental in calculus (and more generally in all mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives. The set of real numbers is denoted or \mathbb and is sometimes called "the reals". The adjective ''real'' in this context was introduced in the 17th century by René Descartes to distinguish real numbers, associated with physical reality, from imaginary numbers (such as the square roots of ), which seemed like a theoretical contrivance unrelated to physical reality. The real numbers include the rational numbers, such as the integer and the fraction . The rest of the real number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
