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Elements of kinematics diagrams include the frame, which is the frame of reference for all the moving components, as well as links (kinematic pairs), and joints. Primary Joints include pins, sliders and other elements that allow pure rotation or pure linear motion. Higher order joints also exist that allow a combination of rotation or linear ...
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
For a system of N particles in 3D real coordinate space, the position vector of each particle can be written as a 3-tuple in Cartesian coordinates: = (,,), = (,,), = (,,) Any of the position vectors can be denoted r k where k = 1, 2, …, N labels the particles.
Kinematics is used in astrophysics to describe the motion of celestial bodies and collections of such bodies. In mechanical engineering, robotics, and biomechanics, [7] 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.
With respect to a coordinate frame whose origin coincides with the body's center of mass for τ() and an inertial frame of reference for F(), they can be expressed in matrix form as:
A space curve; the vectors T, N, B; and the osculating plane spanned by T and N. In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a differentiable curve in three-dimensional Euclidean space, or the geometric properties of the curve itself irrespective of any motion.
Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies. Velocity is a physical vector quantity: both magnitude and direction are needed to define it.
In geometry and kinematics, coordinate systems are used to describe the (linear) position of points and the angular position of axes, planes, and rigid bodies. [16] In the latter case, the orientation of a second (typically referred to as "local") coordinate system, fixed to the node, is defined based on the first (typically referred to as ...