PHYS 1111L Lecture Notes - Lecture 6: Analytical Dynamics, Algebraic Geometry, Mechanical Engineering

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28 Nov 2017
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KINEMATICS
Kinematics is a branch of classical mechanics that describes the motion of points, bodies
(objects), and systems of bodies (groups of objects) without considering the mass of each
or the forces that caused the motion. Kinematics, as a field of study, is often referred to as
the "geometry of motion" and is occasionally seen as a branch of mathematics.A kinematics
problem begins by describing the geometry of the system and declaring the initial conditions
of any known values of position, velocity and/or acceleration of points within the system.
Then, using arguments from geometry, the position, velocity and acceleration of any
unknown parts of the system can be determined. The study of how forces act on masses
falls within kinetics. For further details, see analytical dynamics.
Kinematics is used in astrophysics to describe the motion of celestial bodies and collections
of such bodies. In mechanical engineering, robotics, and biomechanics kinematics is used to
describe the motion of systems composed of joined parts (multi-link systems) such as an
engine, a robotic arm or the human skeleton.
Geometric transformations, also called rigid transformations, are used to describe the
movement of components in a mechanical system, simplifying the derivation of the equations
of motion. They are also central to dynamic analysis.
Kinematic analysis is the process of measuring the kinematic quantities used to describe
motion. In engineering, for instance, kinematic analysis may be used to find the range of
movement for a given mechanism, and working in reverse, using kinematic synthesis to
design a mechanism for a desired range of motion. In addition, kinematics applies algebraic
geometry to the study of the mechanical advantage of a mechanical system or mechanism.
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