Kinematics
<p><b>Kinematics</b> is the branch of <a href="https://en.wikipedia.org/wiki/Classical_mechanics" title="Classical mechanics">classical mechanics</a> which describes the <a href="https://en.wikipedia.org/wiki/Motion_%28physics%29" title="Motion (physics)">motion</a> of points (alternatively "particles"), bodies (objects), and systems of bodies without consideration of the masses of those objects nor the forces that may have caused the motion.<a href="https://en.wikipedia.org/wiki/Kinematics#cite_note-Whittaker-1"><sup id="cite_ref-Whittaker_1-0" class="reference">[1]</sup></a><a href="https://en.wikipedia.org/wiki/Kinematics#cite_note-Beggs-2"><sup id="cite_ref-Beggs_2-0" class="reference">[2]</sup></a><a href="https://en.wikipedia.org/wiki/Kinematics#cite_note-Wright-3"><sup id="cite_ref-Wright_3-0" class="reference">[3]</sup></a> </p>
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Kinematics as a field of study is often referred to as the "geometry of motion" and as such may be seen as a branch of mathematics.<sup id="cite_ref-4" class="reference"><a href="https://en.wikipedia.org/wiki/Kinematics#cite_note-4">[4]</a></sup><sup id="cite_ref-5" class="reference"><a href="https://en.wikipedia.org/wiki/Kinematics#cite_note-5">[5]</a></sup><sup id="cite_ref-6" class="reference"><a href="https://en.wikipedia.org/wiki/Kinematics#cite_note-6">[6]</a></sup> Kinematics begins with a description of the geometry of the system and the initial conditions of known values of the position, velocity and or acceleration of various points that are a part of the system, then from geometrical arguments it can determine the position, the velocity and the acceleration of any part of the system. The study of the influence of forces acting on masses falls within the purview of <a href="https://en.wikipedia.org/wiki/Kinetics_%28physics%29" title="Kinetics (physics)">kinetics</a>. For further details, see <a href="https://en.wikipedia.org/wiki/Analytical_dynamics" title="Analytical dynamics">analytical dynamics</a>.
Kinematics is used in <a href="https://en.wikipedia.org/wiki/Astrophysics" title="Astrophysics">astrophysics</a> to describe the motion of <a href="https://en.wikipedia.org/wiki/Celestial_bodies" class="mw-redirect" title="Celestial bodies">celestial bodies</a> and collections of such bodies. In <a href="https://en.wikipedia.org/wiki/Mechanical_engineering" title="Mechanical engineering">mechanical engineering</a>, <a href="https://en.wikipedia.org/wiki/Robotics" title="Robotics">robotics</a>, and <a href="https://en.wikipedia.org/wiki/Biomechanics" title="Biomechanics">biomechanics</a><sup id="cite_ref-Biewener_7-0" class="reference"><a href="https://en.wikipedia.org/wiki/Kinematics#cite_note-Biewener-7">[7]</a></sup> kinematics is used to describe the motion of systems composed of joined parts (multi-link systems) such as an <a href="https://en.wikipedia.org/wiki/Engine" title="Engine">engine</a>, a <a href="https://en.wikipedia.org/wiki/Robot_kinematics" title="Robot kinematics">robotic arm</a> or the <a href="https://en.wikipedia.org/wiki/Human_skeleton" title="Human skeleton">skeleton</a> of the human body.
The use of geometric transformations, also called <a href="https://en.wikipedia.org/wiki/Rigid_transformation" title="Rigid transformation">rigid transformations</a>, to describe the movement of components of a <a href="https://en.wikipedia.org/wiki/Mechanical_system" title="Mechanical system">mechanical system</a> simplifies the derivation of its equations of motion, and is central to <a href="https://en.wikipedia.org/wiki/Lagrangian_mechanics" title="Lagrangian mechanics">dynamic analysis</a>.
<a href="https://en.wikipedia.org/wiki/Robot_kinematics" title="Robot kinematics">Kinematic analysis</a> is the process of measuring the <a href="https://en.wikipedia.org/wiki/Physical_quantity" title="Physical quantity">kinematic quantities</a> used to describe motion. In engineering, for instance, kinematic analysis may be used to find the range of movement for a given <a href="https://en.wikipedia.org/wiki/Mechanism_%28engineering%29" title="Mechanism (engineering)">mechanism</a>, and working in reverse, using <a href="https://en.wikipedia.org/wiki/Burmester_theory" class="mw-redirect" title="Burmester theory">kinematic synthesis</a> used to design a mechanism for a desired range of motion.<sup id="cite_ref-McCarthy2010_8-0" class="reference"><a href="https://en.wikipedia.org/wiki/Kinematics#cite_note-McCarthy2010-8">[8]</a></sup> In addition, kinematics applies <a href="https://en.wikipedia.org/wiki/Algebraic_geometry" title="Algebraic geometry">algebraic geometry</a> to the study of the <a href="https://en.wikipedia.org/wiki/Mechanical_advantage" title="Mechanical advantage">mechanical advantage</a> of a <a href="https://en.wikipedia.org/wiki/Mechanical_system" title="Mechanical system">mechanical system</a> or mechanism.</p>