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For two-dimensional, plane strain problems the strain-displacement relations are = ; = [+] ; = Repeated differentiation of these relations, in order to remove the displacements and , gives us the two-dimensional compatibility condition for strains
The coordinates of points in a plane are two-dimensional vectors in R 2 (two dimensional space). Rigid transformations are those that preserve the distance between any two points. The set of rigid transformations in an n-dimensional space is called the special Euclidean group on R n, and denoted SE.
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 ...
In fluid mechanics, a two-dimensional flow is a form of fluid flow where the flow velocity at every point is parallel to a fixed plane. The velocity at any point on a ...
Paden–Kahan subproblems are a set of solved geometric problems which occur frequently in inverse kinematics of common robotic manipulators. [1] Although the set of problems is not exhaustive, it may be used to simplify inverse kinematic analysis for many industrial robots. [2]
A top Federal Reserve official said Monday that he is leaning toward supporting an interest rate cut when the Fed meets in two weeks but that evidence of persistent inflation before then could ...
In analytical mechanics, a branch of applied mathematics and physics, a virtual displacement (or infinitesimal variation) shows how the mechanical system's trajectory can hypothetically (hence the term virtual) deviate very slightly from the actual trajectory of the system without violating the system's constraints.