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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.
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. [8] In addition, kinematics applies algebraic geometry to the study of the mechanical advantage of a mechanical system or mechanism.
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 ...
The first step in the process is to show that this condition implies that the infinitesimal rotation tensor is uniquely defined. To do that we integrate ∇ w {\displaystyle {\boldsymbol {\nabla }}\mathbf {w} } along the path X A {\displaystyle \mathbf {X} _{A}} to X B {\displaystyle \mathbf {X} _{B}} , i.e.,
The kinematics equations for the series chain of a robot are obtained using a rigid transformation [Z] to characterize the relative movement allowed at each joint and separate rigid transformation [X] to define the dimensions of each link. The result is a sequence of rigid transformations alternating joint and link transformations from the base ...
Screw theory is the algebraic calculation of pairs of vectors, also known as dual vectors [1] – such as angular and linear velocity, or forces and moments – that arise in the kinematics and dynamics of rigid bodies.
The input-output equations of a spherical four-bar linkage can be applied to spatial four-bar linkages when the variables are replaced by dual numbers. [8] Note that the cited conference paper incorrectly conflates Moore-Penrose pseudoinverses with one-sided inverses of matrices, falsely claiming that the latter are unique whenever they exist.
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.