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[4] [5] [6] 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.
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.
From this point of view the kinematics equations can be used in two different ways. The first called forward kinematics uses specified values for the joint parameters to compute the end-effector position and orientation. The second called inverse kinematics uses the position and orientation of the end-effector to compute the joint parameters ...
It is common practice to design the linkage system so that the movement of all of the bodies are constrained to lie on parallel planes, to form what is known as a planar linkage. It is also possible to construct the linkage system so that all of the bodies move on concentric spheres, forming a spherical linkage .
The transport theorem (or transport equation, rate of change transport theorem or basic kinematic equation or Bour's formula, named after: Edmond Bour) is a vector equation that relates the time derivative of a Euclidean vector as evaluated in a non-rotating coordinate system to its time derivative in a rotating reference frame.
In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body. They are named in honour of Leonhard Euler. Their general vector form is
Classical mechanics utilises many equations—as well as other mathematical concepts—which relate various physical quantities to one another. These include differential equations , manifolds , Lie groups , and ergodic theory . [ 4 ]
The first of these equations express the Newton's law and is the equivalent of the vector equation = (force equal mass times acceleration) plus = ˙ + (angular acceleration in function of inertia and angular velocity); the second equation permits the evaluation of the linear and angular momentum when velocity and inertia are known.