Minimal Representations of a Face of a Convex Polyhedron and Some Applications

In this paper, we propose a method for determining all minimal representations of a face of a polyhedron defined by a system of linear inequalities. Main difficulties for determining prime and minimal representations of a face are that the deletion of one redundant constraint can change the redundancy of other constraints and the number of descriptor index pairs for the face can be huge. To reduce computational efforts in finding all minimal representations of a face, we prove and use properties that deleting strongly redundant constraints does not change the redundancy of other constraints and all minimal representations of a face can be found only in the set of all prime representations of the face corresponding to the maximal descriptor index set for it. The proposed method is based on a top-down search strategy, is easy to implement, and has many computational advantages. Based on minimal representations of a face, a reduction of degeneracy degrees of the face and ideas to improve some known methods for finding all maximal efficient faces in multiple objective linear programming are presented. Numerical examples are given to illustrate the method.

A self-adjusting stiffness center design for large stroke compliant XY nanomanipulators

In the present paper, it is proposed a self-adjusting stiffness center (SASC) design for large stroke XY beam flexure-based mechanisms. An important feature of the SASC lies in it restricts the in-plane parasitic rotation by reducing the moment of force instead of increasing the rotational stiffness widely utilized in the literature. Specifically, it is shown that by leveraging on the varied stiffness of the parallelogram flexure, the stiffness center can be made stationary by appropriately setting the relevant geometric parameters, so that the parasitic rotation can be restricted. Furthermore, it is presented a millimeter stroke XY nanomanipulator with the SASC-based redundant constraint in a case study. Numerous finite element analysis (FEA) results demonstrate that the proposed design is not only capable of achieving 1.5 × 1.5 mm2 working range in a compact desktop size, but significantly reduces the in-plane moment applied to the motion stage. The proposed SASC-based design provides an alternative approach to reduce the parasitic rotation of large stroke XY beam flexure-based mechanisms.

A method of redundant constraint elimination in the problem of body recovery based on support function measurements

Предложен новый алгоритм восстановления тел по измерениям их опорных функций, который представляет собой алгоритм квадратичного или линейного программирования в форме Гарднера-Кидерлена с меньшим числом ограничений. Уменьшение числа ограничений достигается за счет нового метода, который позволяет исключить из исходной системы ограничений часть ограничений как избыточные. Предложен новый подход, позволяющий применять методы восстановления тел по измерениям опорной функции к задаче восстановления тел по теневым контурам. Представлено описание реализации алгоритма, а также результаты его тестирования на реальных промышленных теневых контурах. Предложенный метод в рассмотренном примере позволил сократить число ограничений на 80% и ускорить исходный алгоритм Гарднера-Кидерлена на порядок. A new body recovery algorithm based on support function measurements is proposed. The proposed algorithm represents a linear or quadratic programming problem in Gardner-Kiderlen form with smaller number of constraints. The reduction of constraint number is based on a new method that allows one to eliminate a part of initial constraints as redundant. A new approach of body recovery based on shadow contours is proposed. It allows one to reuse body recovery methods based on support function measurements. The implementation of the algorithm is described and some results of its testing on real industrial contours are discussed. The proposed method ensures the reduction of constraint number by 80% in the discussed example and also enables to speedup the initial Gardner-Kiderlen algorithm by an order of magnitude.

Study on Redundant Constraint in Mechanism Design

Two kinds of redundant constraints in mechanism and the application are discussed in this article.The calculation method of degree of freedom are given about two kinds of redundant constraints. The roles of redundant constraint for mechanism s function is analysed.Some questions is noticed in mechanism design.

A Novel Compliant Mechanism with Three Degrees of Freedom

A novel compliant mechanism with three degree of freedom (DOF) is proposed, based on the method of Freedom and Constraint Topology (FACT). One movement and two rotations are obtained in Case 3, Type 2 freedom space. A redundant constraint is added to improve the symmetry. The finite element modal (FEM) is established and static force analysis is conducted. Results demonstrate that the compliant mechanism is decoupled. Modal analysis is carried out with the finite element method. And four orders natural frequency and main vibration mode are obtained.