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Every vector space is a free module, [1] but, if the ring of the coefficients is not a division ring (not a field in the commutative case), then there exist non-free modules. Given any set S and ring R, there is a free R-module with basis S, which is called the free module on S or module of formal R-linear combinations of the elements of S.
The development of MOOSE at Idaho National Laboratory (INL) since May 2008, has resulted in a unique approach to computational engineering that combines computer science with a strong underlying mathematical description in a unique way that allows scientists and engineers to develop engineering simulation tools in a fraction of the time previously required. [2]
A manipulator can move an object with up to 6 degrees of freedom (DoF), determined by 3 translation 3T and 3 rotation 3R coordinates for full 3T3R mobility. However, when a manipulation task requires less than 6 DoF, the use of lower mobility manipulators, with fewer than 6 DoF, may bring advantages in terms of simpler architecture, easier control, faster motion and lower cost. [2]
In robotics, a manipulator is a device used to manipulate materials without direct physical contact by the operator. The applications were originally for dealing with radioactive or biohazardous materials, using robotic arms , or they were used in inaccessible places.
Download QR code; Print/export Download as PDF; Printable version ... In mathematics, a stably free module is a module which is close to being free. Definition. A ...
The Fuller calculator, sometimes called Fuller's cylindrical slide rule, is a cylindrical slide rule with a helical main scale taking 50 turns around the cylinder. This creates an instrument of considerable precision – it is equivalent to a traditional slide rule 25.40 metres (1,000 inches) long.
for a module M and free module F. If the kernel of φ is finitely generated, then M is called a finitely related module. Since M is isomorphic to F/ker(φ), this basically expresses that M is obtained by taking a free module and introducing finitely many relations within F (the generators of ker(φ)).
For serial manipulators this requires solution of a set of polynomials obtained from the kinematics equations and yields multiple configurations for the chain. The case of a general 6R serial manipulator (a serial chain with six revolute joints ) yields sixteen different inverse kinematics solutions, which are solutions of a sixteenth degree ...