Euclidean Space

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euclidean space

[yü′klid·ē·ən ′spās]
A space consisting of all ordered sets (x1, …, xn ) of n numbers with the distance between (x1, …, xn ) and (y1, …, yn ) being given by the number n is called the dimension of the space.

Euclidean Space


in mathematics, a space whose properties are described by the axioms of Euclidean geometry. In a more general sense, a Euclidean space is an n-dimensional vector space, into which several special Cartesian coordinates can be introduced so that its metric is defined in the following manner: If point M has the coordinates (x1x2, …, xn and point M* has the coordinates (x1*, x2*, …, xn*), then the distance between these points is

References in periodicals archive ?
In order to pass from Cartesian space to joint space in terms of position, velocity and acceleration the inverse kinematics is required.
We define generalised Cartesian space coordinates p, whose elements are the six variables chosen to describe the position and orientation of the platform, as p = f (x, y, z, [phi], [theta], [psi]).
So, the reference coordinates of linear actuators can be computed with (5) for a position of the end-effector in cartesian space.