This paper presents a new approach for the determination of 3 − RPR planar parallel robot assembly modes. In this approach, the parallel robot is considered as a multi robot system. The segments are then regarded as serial robots moving a common load. The proposed approach is based on a parallel robot Jacobian matrix factorization. This factorization is an extension of global formalism develope...

Mario A. Garcia-Murillo 1,*, Roger E. Sanchez-Alonso 2 and Jaime Gallardo-Alvarado 3 1 Department of Mechanical Engineering, DICIS, Universidad de Guanajuato, Salamanca 36885, GTO, Mexico 2 Universidad Nacional de Ingeniería (UNI), Managua 5595, Nicaragua; [email protected] 3 Department of Mechanical Engineering, Instituto Tecnológico de Celaya, Celaya 38010, GTO, Mexico; jaime.gallardo@i...

Parallel mechanisms frequently contain an unstable type of singularity that has no counterpart in serial mechanisms. When the mechanism is at or near this type of singularity, it loses the ability to counteract external forces in certain directions. This paper considers the application of additional kinematic constraint through passive joint braking in the close neighborhood of unstable poses. ...

In this paper we study the planar graphs that admit an acyclic 3-coloring. We show that testing acyclic 3-colorability is NP-hard, even for planar graphs of maximum degree 4, and we show that there exist infinite classes of cubic planar graphs that are not acyclically 3-colorable. Further, we show that every planar graph has a subdivision with one vertex per edge that admits an acyclic 3-colori...

A parallel manipulator provides an alternative design to serial manipulators, and can be found in many applications such as mining machines (Arai et al., 1991). Through the design of active joints such that actuators are fixed to the manipulator base, the mass of moving components of the parallel manipulator is greatly reduced, and high speed and high acceleration performance may be achieved. P...

We present a linear work parallel iterative algorithm for solving linear systems involving Laplacians of planar graphs. In particular, if Ax = b, where A is the Laplacian of any planar graph with n nodes, the algorithm produces a vector x̄ such that ||x − x̄||A ≤ , in O(n log(1/ )) parallel time, doing O(n log(1/ )) work, where c is any positive constant. One of the key ingredients of the solver,...

We present a linear work parallel iterative algorithm for solving linear systems involving Laplacians of planar graphs. In particular, if Ax = b, where A is the Laplacian of any planar graph with n nodes, the algorithm produces a vector x̄ such that ||x − x̄||A ≤ ǫ, in O(n log(1/ǫ)) parallel time, doing O(n log(1/ǫ)) work, where c is any positive constant. One of the key ingredients of the solver...

We present a linear work parallel iterative algorithm for solving linear systems involving Laplacians of planar graphs. In particular, if Ax = b, where A is the Laplacian of any planar graph with n nodes, the algorithm produces a vector x̄ such that ||x − x̄||A ≤ ǫ, in O(n log(1/ǫ)) parallel time, doing O(n log(1/ǫ)) work, where c is any positive constant. One of the key ingredients of the solver...