Smoothly shaded renderings of polyhedral objects on raster displays

1979 ◽  
Author(s):  
Tom Duff
Keyword(s):  
Polyhedral Objects

Formation of Geometric Tolerance Zones for Polyhedral Objects

1997 ◽  
Author(s):  
Utpal Roy ◽  
Bing Li
Keyword(s):  
Variational Model ◽  
Tolerance Zone ◽  
Geometric Tolerance ◽  
Geometric Tolerances ◽  
Polyhedral Objects ◽  
Different Types ◽  
Tolerance Zones ◽  
Algebraic Constraints ◽  
Size Tolerance ◽  
Part Model

Abstract This paper presents a scheme for establishing geometric tolerance zones for polyhedral objects in solid modelers. The proposed scheme is based on a surface-based variational model. Variations are applied to a part model by varying each surface’s model variables. Those model variables are constrained by some algebraic relations derived from the specified geometric tolerances. For size tolerance, two types of tolerance zones are considered in order to reflect two different types of size tolerances. For any other geometric tolerance (form, orientation or positional), the resultant tolerance zone is defined by the combination of size tolerance and that particular geometric tolerance specifications. Appropriate algebraic constraints (on the model variables) are finally used to establish the tolerance zone boundaries in the surface-based variational model.

FEG structures for representation and recognition of 3-D polyhedral objects

1996 ◽  
Vol 18 (3) ◽  
pp. 211-232 ◽  
Author(s):  
Ilan Schreiber ◽  
Moshe Ben-Bassat
Keyword(s):  
Polyhedral Objects

Introducing a Projection-Based Method to Compare Three Approaches Computing the Accumulation of Geometric Variations

2018 ◽  
Author(s):  
Vincent Delos ◽  
Santiago Arroyave-Tobón ◽  
Denis Teissandier
Keyword(s):  
Degrees Of Freedom ◽  
Mechanical Design ◽  
Geometric Constraints ◽  
Computational Time ◽  
Manufacturing Defects ◽  
Design Tolerance ◽  
Polyhedral Objects ◽  
The Difference ◽  
Bounded Sets ◽  
Accumulation Of Defects

In mechanical design, tolerance zones and contact gaps can be represented by sets of geometric constraints. For computing the accumulation of possible manufacturing defects, these sets have to be summed and/or intersected according to the assembly architecture. The advantage of this approach is its robustness for treating even over-constrained mechanisms i.e. mechanisms in which some degrees of freedom are suppressed in a redundant way. However, the sum of constraints, which must be computed when simulating the accumulation of defects in serial joints, is a very time-consuming operation. In this work, we compare three methods for summing sets of constraints using polyhedral objects. The difference between them lie in the way the degrees of freedom (DOFs) (or invariance) of joints and features are treated. The first method proposes to virtually limit the DOFs of the toleranced features and joints to turn the polyhedra into polytopes and avoid manipulating unbounded objects. Even though this approach enables to sum, it also introduces bounding or cap facets which increase the complexity of the operand sets. This complexity increases after each operation until becoming far too significant. The second method aims to face this problem by cleaning, after each sum, the calculated polytope to keep under control the effects of the propagation of the DOFs. The third method is new and based on the identification of the sub-space in which the projection of the operands are bounded sets. Calculating the sum in this sub-space allows reducing significantly the operands complexity and consequently the computational time. After presenting the geometric properties on which the approaches rely, we demonstrate them on an industrial case. Then we compare the computation times and deduce the equality of the results of all the methods.

Strategy investigation of precise robotic assembly operations with symmetric regular polyhedral objects

1998 ◽  
Vol 212 (7) ◽  
pp. 571-589 ◽  
Author(s):  
H Qiao ◽  
S K Tso
Keyword(s):  
Contact Forces ◽  
Robotic Assembly ◽  
Coordinate Frame ◽  
Force Sensors ◽  
General Strategy ◽  
Actual Movement ◽  
Polyhedral Objects ◽  
Assembly Operations

In this paper, a general strategy for the precise robotic assembly of symmetrical regular polyhedral objects is presented, according to the character of the objects being assembled. The assembly operations with force sensors included are discussed. The general strategy of the operations with force sensors included is first developed. The assembly operations without relying on force sensors are next analysed. This method can be generally used in industry for the precise assembly operations for symmetric regular polyhedral objects. This paper covers the following items: An important problem demanding solution in the general robotic assembly operations with force sensors is presented. The general strategy investigation for the assembly operations with force sensors included is analysed. The mappings, firstly, between the directions of the contact forces and the location of the peg in the hole coordinate frame and, secondly, between the input forces and the actual movement of the peg in the hole coordinate frame are obtained. The general strategy investigation for the robotic assembly operations for symmetric regular polyhedral objects without using force sensors is designed on the basis of the mappings and the general principles in the strategy investigation. The experiments on the precise round and triangular peg—hole systems are presented to prove the validity of the general strategies designed. The strategy of assembly operations for other symmetric regular polyhedral objects without using force sensors is presented.

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