Describe the following three types of solid models, mention some advantages or disadvantages for each:
- Decomposition models
- Constructive models
- Boundary representation
Decomposition models:
- Can be made of
——Voxels: the solid is composed of a number of cubes
——Cell based: the solid is built up by polygons
- It is an approximate model and requires a lot of memory for high precision
- It is suitable for different types of calculations
Constructive models:
- Solid models are created by manipulating primitives with boolean operators
- It is hard to handle general surfaces
- It is very compact (do not require a lot of memory)
Boundary representation
- The solid is defined with points, curves and surfaces plus a definition of what is inside the model
- Uses graphical methods e.g. sweep and rotate
- Can use parametric surfaces
- Can use Boolean methods
Curves used in geometry modeling can be of different order. What are the advantages and disadvantages of higher order curves?
Advantage: Increased precision
Disadvantages: Risk for corrupt curves, increased calculation time
What is a digital mockup (DMU) and for what is it used?
- A special type of component based assembly model developed to be able to handle large assemblies (>1000 parts) from different CAD-systems
- Can be used for e.g. packaging studies and assembly simulation but not for e.g. calculation of mass etc.
Describe the steps necessary to create a solid, using surface modeling, in a modern CAD system
- Create wireframe elements (points, lines, planes, curves) in 3D or sketches
- Create surfaces from the wireframe geometries (sweep, revolve, …)
- Trim the surfaces together
- Join the surfaces together to a uniform element
- Transform into a solid (Thick, Closed Shalfurface, …)
- (Add fillets)
Describe how trimmed parametric surfaces are defined/created
- Parametric surfaces are defined in a similar way as parametric curves but with two parameters u and v.
- Parametric curves are defined in the same 2D parametric space.
——-They are used to create holes (inner trim curves)
——Or the outer boundary of the surface (outer trim curve) - The trimmed parametric surface is transformed to 3D space
Bézier and B-spline are two types of curves used in geometry modeling. What is the advantage of B-spline curves?
- Better local control of the curve
- Order of the polynomial does not increase with the number of control points
- Easier to define joined curve segments
Mention three different aspects that have to be included in an assembly model (in e.g. a CAD system)
An assembly model needs to include:
- Hierarchical relations
—— assembly -> sub-assembly -> part
- Mating conditions
—— geometrical restrictions, etc
- Mechanical degrees of freedom
Mention two advantages of using solid models instead of e.g. surface models.
- Solid models support higher levels of functionality and automation than surface models
-Example Calculation of mass and moments of inertia - Solid models allow the designer to work with higher level objects rather than points, curves and surfaces
Describe how solid models are created with CSG (Constructive Solid Geometry)
Solid models are created by manipulating “primitives” with Boolean operators (union, sections, subtraction).
In CSG the concept of half spaces is used. Describe/exemplify how they work and how they are used to define geometry
Real analytical functions f(x, y, z) defined in 3D which splits the space in two half spaces:
- One half space where f(x, y, z) <0
- One half space where f(x, y, z) >0
What characterizes a feature ( in the geometry modeling context)?
A feature:
- is a physical part of a detail
- can be linked to a generic form
- has a specific engineering role (function, manufacturing method, simulation method, …)
- has predictable properties
Bézier curves are defined by the following equation:
Se bild!
Describe the different components (of the Bézier equation) of the formula and what they are used for
P_i: control points, defines the curve
B_i,n: weight functions, defines how the different control points affect the curve
n: Order of the curve
n+1: number of control points
What do C^0, C^1 and C^2 continuity between two curve segments mean?
C^0-continuity:
Two curve segments are joined without constraints
C^1-continuity:
The curve segments have the same direction at the common point
C^2-continuity:
The curve segments have the same curvature at the common point
Se bild!
Mention two different usages of geometry models within production
- Ergonomic simulation
- Off-line programming of industrial robots
- Off-line programming of NC-machines
- Off-line programming of CMMs
NURBS is the most commonly used type of curves in modern CAD systems. What geometrical forms can be represented with NURBS but not with Bézier or B-splines?
Bézier and B-splines cannot represent conical and circular forms exactly
Describe the RGB colour model
The colour is accomplished with a mixture of three primary colours
- Red [0 – 1]
- Green [0 – 1]
- Blue [0 – 1]
Mention two different usages of geometry models within production
Ergonomic simulation
Off-line programming of industrial robots, NC-machines, CMMs
