In this article the description of some types of spatial gear constraints (spur gears, bevel gears, etc.) in absolute coordinates is considered. Instead of the numerical expensive calculation of constraint Jacobian matrix we propose to use the transformed Jacobian matrix, which can be calculated much more efficiently. The proposed methods of description of gear constraints were implemented for ...

It is well known that Newton’s method for a nonlinear system has quadratic convergence when the Jacobian is a nonsingular matrix in a neighborhood of the solution. Here we present a modification of this method for nonlinear systems whose Jacobian matrix is singular. We prove, under certain conditions, that this modified Newton’s method has quadratic convergence. Moreover, different numerical te...

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...

Simulations and optimizations are carried out to investigate real-world problems in science and engineering. For instance, solving systems of linear equations with sparse Jacobian matrices is mandatory when using a Newton-type algorithm. The sparsity of Jacobian matrices is exploited and only a subset of the nonzero elements is determined to successfully reduce the usage of the restricting reso...

This paper presents a new context for using the sparse Broyden update method to solve systems of nonlinear equations. The setting for this work is that a Newton-like algorithm is assumed to be available which incorporates a workable strategy for improving poor initial guesses and providing a satisfactory Jacobian matrix approximation whenever required. The total cost of obtaining each Jacobian ...

The kinematics problem is defined as the transformation from the Cartesian space to the joint space and vice versa. Both forward and inverse kinematics solutions for the TR 4000 educational robot arm are presented. The closed form solution of the inverse kinematics problem is of utmost importance in controlling robotic manipulator. In this paper, a closed form solution to the inverse kinematics...

In this paper, some definitions and traditional formulas for calculating the mobility of mechanisms are represented, e.g. Grubler formula, Somov - Malyshev formula, and Buchsbaum - Freudenstei. It is discussed that there are certain cases in which they are too ambiguous and incorrect to use. However, a matrix method is suggested based on the rank of the Jacobian of the mechanism and its applica...

Paper presents a transputerised multi-microprocessor acquisition and processing system, which provides the implementation of the control algorithm in Carthesian coordinates of the position of contour path robots. This based on real-time digital processing of the Jacobian matrix obtained from direct kinematics model, respectively of the inverse Jacobian matrix for close loop control of the posit...

The articulated arm coordinate measuring machine (AACMM) is a kind of new coordinate measuring device based on non-Cartesian system. The measuring accuracy of the AACMM can be effectively improved by parameter identification. However, some of the structural parameters are coupling (linearly related), so the structural parameters usually cannot be identified correctly. The Jacobian matrix was ob...

DSJM is a software toolkit written in portable C++ that enables direct determination of sparse Jacobian matrices whose sparsity pattern is a priori known. Using the seed matrix S ∈ Rn×p, the Jacobian A ∈ Rm×n can be determined by solving AS = B, where B ∈ Rm×p has been obtained via finite difference approximation or forward automatic differentiation. Seed matrix S is defined by the nonzero unkn...