In this paper the trajectory planning problem is solved for a 2PRR parallel manipulator which works in cooperation with a 1 degree-of-freedom (dof) platform. The whole kinematic chain is considered as a redundant 3-dof manipulator, and an algorithm is presented to solve the redundancy by using the joint velocities in the null space of the jacobian matrix. The internal motion of the assisted man...

The Jacobian-free Newton-Krylov method is widely used in solving nonlinear equations arising in many applications. However, an effective preconditioner is required each iteration and determining such may be hard or expensive. In this paper, we propose an efficient two-sided bicoloring method to determine the lower triangular half of the sparse Jacobian matrix via automatic differentiation. Then...

A 2D implicit compact scheme solver has been implemented for the vorticity–velocity formulation in the case of nonreacting, multicomponent, axisymmetric, low Mach number flows. To stabilize the discrete boundary value problem, two sets of boundary closures are introduced to couple the velocity and vorticity fields. A Newton solver is used for solving steady-state and time-dependent equations. I...

In the context of a parallel manipulator, inverse and direct Jacobian matrices are known to contain information which helps us identify some of the singular configurations. In this article, we employ kinematic analysis for the Delta robot to derive the velocity of the end-effector in terms of the angular joint velocities, thus yielding the Jacobian matrices. Setting their determinants to zero, ...

In this pedagogical article, we present a simple direct matrix method for analytically computing the Jacobian of nonlinear algebraic equations that arise from the discretization of nonlinear integro-differential equations. The method is based on a formulation of the discretized equations in vector form using only matrix-vector products and componentwise operations. By applying simple matrix-bas...

It has been established that the second-order stochastic gradient descent (2SGD) method can potentially achieve generalization performance as well as empirical optimum in a single pass (i.e., epoch) through the training examples. However, 2SGD requires computing the inverse of the Hessian matrix of the loss function, which is prohibitively expensive. This paper presents Periodic Step-size Adapt...

This paper is concerned with the development of the Newton–Arithmetic Mean method for large systems of nonlinear equations with block–partitioned jacobian matrix. This method is well suited for implementation on a parallel computer; its degree of decomposition is very high. The convergence of the method is analysed for the class of systems whose jacobian matrix satisfies an affine invariant Lip...

The combined use of Variable Geometry Turbine (VGT) and Exhaust Gas Recirculation (EGR) gives us an opportunity to reduce emissions, without compromising the need to generate more power. In the present work, a multivariable approach is used to tackle the EGR-VGT actuator control problem. A linear multivariable controller is designed using Lyapunov’s Indirect Method, based on the Jacobian matrix...

This paper discusses the feasibility of high-frequency nonlinear vibrational control. Such control has the advantage that it does not require state measurement and processing capabilities that are required in conventional feedback control. Bellman et al. [1] investigated nonlinear systems controlled by linear vibrational controllers and proved that vibrational control is not feasible if the Jac...

The rapid and accurate computation of the Jacobian matrix, which is usually computationally intensive, is of critical importance for the reconstruction problem of fluorescent molecular tomography (FMT). An extension of the Green's function method for the Jacobian matrix computation suitable for two coupled differential equations is proposed, in combination with the parallel forward computing st...