Why are conventional curves, such as y=f(x) or f(x,y)=0, not suitable for CAD?
Since they ar coordinate system depandant and hard to transform
What type of curves should you use when CADing?
Parametric
What are Bézier curves?
An approximate curve where a number of control points defines a characteristic polygon.
The order of the polynomial=number of control points -1
What geometrical forms can’t be represented by Bézier curves och B-splines?
They can’t represent conical and circular forms exactly
Explain the equation for the Bézier curve
Pi: control points, defines the curve
Bi,n: weight functions, defines how the different control points affect the curve
n: order of the curve
n+1: number of control points
u: independant variable 0<=u<=1
What are B-spline curves?
- Further development of Bézier curves. As Bézier they are based on a polygon with a number of control points.
- Allows for better local control of the curve and the order of the polynomial doesn’t increase with the number of control points.
- Makes it easier to define joined curve segments.
- Each segments is controlled by the 4 closes control points.
- For B-splines the weight funtions are more local than for Bézier curves - affects a smaller part of the segment
Explain the equation for the B-spline
n+1: the number of control points
k-1: the order
Nj,k: the weight functions
ti: control point variables
What are NURBS?
- Non-Uniform Rational B-splines
- Bézier and traditional B-splines can’t represent conical and circular forms exactly - rational parametric curves can do this
- Requiers the use of homogenous coordinates
- NURBS is the most commonly used curve type in modern CAD-systems
What are surface models?
- Used in order to be able to create complex, sculptured surface
- Easier to create smooth, complex forms
- ## Commonly used in visualization applications
What are volume/solid models?
- Aims at clearly and information wise completely describe a physical object in a computer
- Solid models support higher levels of functionality and automation than surface models
- Solid models allows the designer to work with higher level objects rather than points, curves and surfaces
What are the requirements on solid models?
- Modeling ability
- Validity
- Clearness and uniquness
- Modeling language
- Compactness
- Computability
What types of solid models are there?
- Decomposition models
- Constructive models
- Boundary representations
What are decomposition models?
- Can be made out of voxels or cell based models
- Voxels: a solid is composed of a number of cubes.
- Cell based models: a solid is build up by polygons
What are some pros and cons with decomposition models?
Pros:
- Good computability
- Suitable for different types of calculations
Cons:
- Is an approximation model
- Requires a lot of memory for high precision
What are constructive models?
Solid models are created by manipulating “primitives” with Boolean operators (union, sections, subtraction)
- Half spaces: solid models are created by combining half spaces with boolean operators
- CSG-models: solid models are created by combining sub-solids in form of parametric primitives (cyliner, sphere, cone…)
What are some pros and cons with constructive models?
Pros:
- It is very compact (do not require a lot of memory)
Cons:
- It is hard to handle general surfaces
What is boundary representation?
- The solid is defined with points, curves and surfaces plus a definition of what is inside the model
- Uses graphical methods such as sweep and rotate
What are some pros and cons with boundary representation?
Pros:
- Can use parametric surfaces
- Can use boolean methods
Cons:
- Low compactness -> more memory is required
Modeling systems based on CSG and boundary representation have important limitations in an engineering context, what are those?
- Requires exact specification of geometry and dimensions
- Tiresome modeling
What is the definition of features?
- Is a physical part of a detail
- Can be linked to a generic form
- Ha a specific engineering role (ex. manufacturing or simulation method)
- Has predictable properties
*A feature based product model describes a part or an assembly in terms of its features
What types of features are there?
- Form features: commonly used shapes
- Tolerance features: deviation from nominal shape, position or orientation
- Assembly features: mating conditions, position and orientation
- Functional features: design intent, non-geometric attributes, performance etc.
- Material features: material composition, surface treatment etc.
What do you need to consider regarding assembly development?
- Kinematics
- Interchangeability/variants of parts
-Geometric layout for effective packaging - Assembleability/deassembleability
- Collisions and interference
- Tolerance chains and tolerance allocation
What does an assembly model need to include?
- Hierarchical relations: assembly -> sub-assemblu -> part
- Mating conditions: geometrical restrictions etc.
- Position and orientation of sub-assemblies and parts, globally and locally
- Mechanical degrees of freedom
