Constructing minimum deflection fixture arrangements using frame invariant norms

This paper describes a fixture planning method that minimizes object deflection under external loads. The method takes into account the natural compliance of the contacting bodies and applies to two-dimensional and three-dimensional quasirigid bodies. The fixturing method is based on a quality measure that characterizes the deflection of a fixtured object in response to unit magnitude wrenches. The object deflection measure is defined in terms of frame-invariant rigid body velocity and wrench norms and is therefore frame invariant. The object deflection measure is applied to the planning of optimal fixture arrangements of polygonal objects. We describe minimum-deflection fixturing algorithms for these objects, and make qualitative observations on the optimal arrangements generated by the algorithms. Concrete examples illustrate the minimum deflection fixturing method. Note to Practitioners-During fixturing, a workpiece needs to not only be stable against external perturbations, but must also stay within a specified tolerance in response to machining or assembly forces. This paper describes a fixture planning approach that minimizes object deflection under applied work loads. The paper describes how to take local material deformation effects into account, using a generic quasirigid contact model. Practical algorithms that compute the optimal fixturing arrangements of polygonal workpieces are described and examples are then presented

Independent contact regions for discretized 3D objects with frictionless contacts

This paper deals with the problem of determining independent contact regions on a 3D object boundary such that a seven finger frictionless grasp with a contact point in each region assures a force-closure grasp on the object, independently of the exact position of the contact points. These regions provide robustness in front of finger positioning errors in grasp and fixturing applications. The object’s structure is discretized in a cloud of points, so the procedure is applicable to objects of any arbitrary shape. The procedure finds an initial form-closure grasp that is iteratively improved through an oriented search procedure: once a locally optimum grasp has been reached, the independent contact regions are computed. The procedure has been implemented, and application examples are included in the paper

Frictionless grasp with 7 fingers on discretized 3D objects

This paper presents an algorithm to plain locally frictionless grasp on 3D objects. The objects can be of any arbitrary shape, since the surface is discretized in a cloud of points. The planning algorithm finds an initial force-closure grasp that is iteratively improved through an oriented search procedure. The grasp quality is measured with the “largest ball” criterion, and a force-closure test based on geometric considerations is used. The efficiency of the algorithm is illustrated through numerical example