The Free Body Diagram method, based on the dynamic equations of isolated rigid bodies, is used to overcome the diiculties in dynamic modeling of legged robots. This article presents a simulator for a six leg machine. Both kinematic and dynamic models are developed. Kinematic equations are derived with Denavit-Hartenberg method. The Free Body Diagram method is used to obtain the dynamic model. S...

A small improvement in the structure of the material could save the manufactory a lot of money. The free material design can be formulated as an optimization problem. However, due to its large scale, secondorder methods cannot solve the free material design problem in reasonable size. We formulate the free material optimization (FMO) problem into a saddle-point form in which the inverse of the ...

In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is symmetric and positive-definite. The conjugate gradient method is often implemented as an iterative algorithm, applicable to sparse systems that are too large to be handled by a direct implementation or other direct methods such as the ...

Given a finite poset P , let La(n, P ) denote the largest size of a family of subsets of an n-set that does not contain P as a (weak) subposet. We employ a combinatorial method, using partitions of the collection of all full chains of subsets of the nset, to give simpler new proofs of the known asymptotic behavior of La(n, P ), as n → ∞, when P is the r-fork Vr, the four-element N poset N , and...

A general equilibrium model for multiphase multicomponent inorganic atmospheric aerosols is proposed. The thermodynamic equilibrium is given by the minimum of the Gibbs free energy for a system involving an aqueous phase, a gas phase and solid salts. A primal-dual algorithm solving the Karush-Kuhn-Tucker conditions is detailed. An active set/Newton method permits to compute the minimum of energ...

In current study, The Mesh-free method based on weak-form formulation coupled with the ultrasound imaging technique is developed. This problem consists in computing the deformation of an elastic non-homogenous phantom by numerical methods (both Mesh-free and Finite Element) and converge their results to the measured deformation by the ultrasound. The shape functions of Mesh-free are approximate...

In this paper, by considering the notion of extended BCK-module, we define the concepts of free extended BCK-module, free object in category of extended BCK-modules and we state and prove some related results. Specially, we define the notion of idempotent extended BCK-module and we get some important results in free extended BCK-modules. In particular, in category of idempotent extended BCK-mod...

We investigate the properties of rigid polyelectrolyte solutions in the presence of monovalent salt. The free energy within the Debye-Hückel-Bjerrum (DHBj) theory (Fisher, M. E.; Levin, Y. Phys. Rev. Lett. 1993, 71, 3826) is constructed. It is found that at thermodynamic equilibrium the polyelectrolyte solution consists of clusters composed of one polyion and various counterions. The distributi...