If the structural stiffness of the parts are sufficient, then their deformation can be neglected and rigid transformations can be used to define this relative movement. The movement of components of a mechanical system are analyzed by attaching a reference frame to each part and determining how the various reference frames move relative to each other. Point trajectories in a body moving in the plane In three dimensions, the position vector r It expresses both the distance of the point from the origin and its direction from the origin. The position vector of a particle is a vector drawn from the origin of the reference frame to the particle. All observations in physics are incomplete without being described with respect to a reference frame. However, if the particle is constrained to move within a plane, a two-dimensional coordinate system is sufficient.

In the most general case, a three-dimensional coordinate system is used to define the position of a particle. If the tower is 50 m high, and this height is measured along the z-axis, then the coordinate vector to the top of the tower is r = (0 m, −50 m, 50 m).

For example, consider a tower 50 m south from your home, where the coordinate frame is centered at your home, such that east is in the direction of the x-axis and north is in the direction of the y-axis, then the coordinate vector to the base of the tower is r = (0 m, −50 m, 0 m). The position of a particle is defined as the coordinate vector from the origin of a coordinate frame to the particle. Particle kinematics is the study of the trajectory of particles. Notice the setup is not restricted to 2-d space, but a plane in any higher dimension. Kinematic vectors in plane polar coordinates. In addition, kinematics applies algebraic geometry to the study of the mechanical advantage of a mechanical system or mechanism. 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. Kinematic analysis is the process of measuring the kinematic quantities used to describe motion. They are also central to dynamic analysis. 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. 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. Kinematics is used in astrophysics to describe the motion of celestial bodies and collections of such bodies. For further details, see analytical dynamics. The study of how forces act on bodies falls within kinetics, not kinematics. Then, using arguments from geometry, the position, velocity and acceleration of any unknown parts of the system can be determined. 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.

Kinematics, as a field of study, is often referred to as the 'geometry of motion' and is occasionally seen as a branch of both applied and pure mathematics since it can be studied without considering the mass of a body or the forces acting upon it. Kinematics is a subfield of physics and mathematics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move.

Cinemática formulas