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...

‎It is shown that the knowledge of a surjective morphism $Xto Y$ of complex‎ ‎curves can be effectively used‎ ‎to make explicit calculations‎. ‎The method is demonstrated‎ ‎by the calculation of $j(ntau)$ (for some small $n$) in terms of $j(tau)$ for the elliptic curve ‎with period lattice $(1,tau)$‎, ‎the period matrix for the Jacobian of a family of genus-$2$ curves‎ ‎complementing the classi...

One of the widely used methods for solving a nonlinear system of equations is the quasi-Newton method. The basic idea underlining this type of method is to approximate the solution of Newton's equation by means of approximating the Jacobian matrix via quasi-Newton update. Application of quasi-Newton methods for large scale problems requires, in principle, vast computational resource to form and...

The mapping between the Cartesian space and joint space of robot manipulators has long been a difficult task for redundant robots. Two main methods are used in the classical approach. One is by using direct kinematic inversion in the position regime; the other is to use Jacobian Transformation in the velocity regime. However, for a redundant robot, a non-squared Jacobian matrix is resulted when...

Inferring dynamics of metabolic networks directly from metabolomics data provides a promising way to elucidate the underlying mechanisms of biological systems, as reported in our previous studies (Weckwerth, 2011; Sun and Weckwerth, 2012; Nägele et al., 2014) by a differential Jacobian approach. The Jacobian is solved from an overdetermined system of equations as JC + CJ(T)  = -2D, called Lyapu...

The mapping between the Cartesian space and joint space of robot manipulators has long been a difficult task for redundant robots. Two main methods are used in the classical approach. One is by using direct kinematic inversion in the position regime; the other is to use Jacobian Transformation in the velocity regime. However, for a redundant robot, a non-squared Jacobian matrix is resulted when...

For differential-algebraic power systems, saddle-noddle bifurcation and Hopf bifurcation are both of universally existent phenomena in power systems. Usually Newton iteration method could be applied to the Moore-Spence system to compute saddle-noddle and Hopf bifurcation points directly. But the Moore-Spence system has very high dimension and causes much complexity in Jacobian matrix factorizat...

For uncalibrated visual servoing for image-based dynamic control of robot manipulators, acquiring an image Jacobian matrix (interaction matrix) or its inverse matrix is necessary and difficult. In this paper, a new controller of uncalibrated visual sevro using pseudo inverse of image Jacobian matrix is presented, which based on dynamics of robot manipulators. In this method, camera’s intrinsic ...

Simulation of nonisothermal, multiphase flow through fractured geothermal reservoirs involves the solution of a system of strongly nonlinear algebraic equations. The Newton-Raphson method used to solve such a nonlinear system of equations requires the evaluation of a Jacobian matrix. In this paper we discuss automatic differentiation (AD) as a method for analytically computing the Jacobian matr...

Traditional kinematic analysis of manipulators, built upon a deterministic articulated kinematic modeling often proves inadequate to capture uncertainties affecting the performance of the real robotic systems. While a probabilistic framework is necessary to characterize the system response variability, the random variable/vector based approaches are unable to effectively and efficiently charact...