Appendix of Geometric Modeling

In this appendix, you will learn how to use the geometric modeling tools available within EMPro.

Editing Cross-Sections for 2-D and 3-D Models

Shapes

Edge tools

Edge tools are used to create lines of various shapes within the EMPro interface. The following figure displays the Edge Tools including the Straight Edge tool (upper left), Polyline Edge tool (upper right), Tangent Line tool (lower left) and Perpendicular Edge tool (lower right).

The Edge Tools

Straight Edge

Creates a simple straight edge. To use this tool, click the Straight Edge button and click two points in the sketching plane where the endpoints should be located.

Polyline Edge

The Polyline Edge is similar to the Straight Edge tool except it allows multiple points to create a series of connected straight edges. Click a starting point in the sketching plane and continue clicking on the locations of subsequent endpoints to create desired polyline edge. Click on the first vertex or press |Return| to finish.

Perpendicular Edge

Creates a straight edge perpendicular to an existing edge. To use, select the Perpendicular Edge button and click on the existing edge that will define the perpendicular direction. This can be a straight or curved edge. Then click on the location of the first and second endpoints of the perpendicular straight edge.

Tangent Line

Similar to the Perpendicular Edge tool, but instead draws a line tangent to a pre-existing, non-linear edge. To use, select the Tangent Line tool, and click on the existing curve that will define the tangential direction. Then click on the location of the first and second endpoints of the tangential straight edge.

Closed Polygon Tools

The following illustration displays the Closed Polygon tools including the Rectangle, Polygon and N-Sided Polygon tools.

The Closed Polygon tools

Rectangle

Creates a simple rectangle. Click the desired location of the first vertex of the rectangle and drag the mouse to the location of the second vertex.

Polygon

Creates a polygon specified by the user. (For regular polygons, see N-Sided Polygon). It functions like the Polyline Edge tool. Click the starting point and all subsequent points, then press |Return| to close the polygon. This will draw a line from the last selected endpoint to the first endpoint.

N-Sided Polygon

Creates a regular, N-Sided Polygon of a user-specified number of sides. Click the location of the center of the polygon. Then press the left-bracket key '[', or the right-bracket key ']' to decrease or increase the number of sides, respectively. Once the correct number of sides is selected, drag the mouse until the desired size and orientation around the center point is achieved and click again to finish the N-sided polygon.

Arc Tools

The figure below displays two of the arc tools: the 3-Point Arc and 2-Point Arc tools.

The Arc tools

3-Point Arc Tool

Creates an open arc from three points. Click on the location of the first endpoint. Click a second location to specify a point between the two endpoints (which helps determine size), and a third location to specify the other endpoint.

2-point Arc Tool

Creates a semi-circle from two points. Click on the first endpoint location and drag the mouse until the desired semi-circle size and orientation is achieved. Click this second end point location to finish.

Arc center, 2 points Tool

Creates an open arc from three points. First, click on the location of the center of the arc. Secondly, click a point to specify the radius of the arc. Finally, click the location of the endpoint to specify the length of the arc.

Circle and Ellipse Tools

The following figure displays an example of a circle drawn with the Circle Center, Radius tool.

A circle drawn with Circle Center, Radius tool

Circle Center, Radius

Creates a circle defined by its center point and radius. Click the location of the circle's center point, then select another point to define the radius and finish the circle.

3-point Circle

Creates a circle based on three user-specified points, similar to the 3-Point Arc tool. Click the first two points to set the location of the circle and the third to specify its size.

2-point Circle

Creates a circle based on the distance between two points. After selecting the first point, choose the second to define the diameter and finish the circle.

Ellipse

Draws an ellipse from three points: the center and two perpendicular radii. Click the center point of the ellipse, then select the desired location of the first radii. Finally, select the desired length of the second radii, perpendicular to the first.

Tools

Select/Manipulate

Selects anything within the sketch. This is the default tool when no other tool is selected. It can be used to:

• Move an object, edge, or vertex to a new position, by clicking-and-dragging
• Select a vertex or edge and lock or edit its position, by right-clicking and selecting Lock Position or Edit Position.
• Edit the value of an angle or distance constraint, by right-clicking and selecting the edit option.
• Delete an edge or constraint, by right-clicking and selecting the delete option.

  Select/Manipulate tool

  

Trim Curves

Deletes segments of curves until they intersect with other curves. To use this tool, click on the section of the curve that is to be deleted.

Trim Curves tool

Insert Vertex

Inserts a vertex onto an already existing edge. Click the desired location of the new vertex on the existing edge.

Insert Vertex tool

Fillet Vertex

Converts a sharp corner into a rounded corner between two curves. Click on any sharp corner and drag until the desired fillet radius is achieved and click to finalize fillet.

Fillet Vertex tool

Constraints

The geometry Constraints tools are used to modify pre-drawn shapes to the desired specifications.

Horizontal Constraint

Constrains a segment to the horizontal direction.

Polygon before (left) and after (right) two sides are constrained horizontally

Vertical Constraint

Constrains a segment to the vertical direction.

Polygon before (left) and after (right) two sides are vertically constrained

Collinear Constraint

Constrains two straight segments so that they are in line with each other.

Polygon before (left) and after (right) after two sides are constrained to be collinear

Parallel Constraint

Constrains two straight segments so that they are parallel to each other.

Polygon before (left) and after (right) two sides are constrained in parallel

Perpendicular Constraint

Constrains two straight segments so that they are perpendicular to each other. The following figure displays a polygon before (left) and after (right) two sides are perpendicularly constrained

Tangent Constraint

Constrains a straight segment so that it is tangent to a circular segment at a point. In the following figure, Circle and polygon before (left) and after (right) a side of the polygon is constrained tangentially with reference to the circle:

Concentric Constraint

Constrains two circular segments so that they are centered upon the same point. In the following figure, two circles before (left) and after (right) are made concentric:

Angle Constraint

Constrains an angle to a user-specified value between two straight lines. Click once to select angle, then click a second time to place label and enter the angle size. In the figure below, the polygon before (left) and after (right) an angle has been constrained to a user-defined value.

Distance Constraint

Constrains the distance between two points, the distance between a point and a line, or the length of a line to a user-specified value. After selecting the object(s) to constrain, click a final time to place label and enter distance.

As shown in the figure below, there are three different constraint "modes": parallel, vertical and horizontal. The mode is determined by the location of the mouse cursor when you click to specify where the constraint should be drawn.

The polygon (A) before line has been constrained, (B) with a parallel distance constraint, (C) with a vertical distance constraint and (D) with a horizontal distance constraint.

Equal Length Constraint

Constrains selected segments to an equal length (assumes the length of the segment selected second). Polygon before (left) and after (right) two sides are made equal length to one another.

Equal Distance Constraint

Constrains two pairs of points so that each pair assumes a distance from each other equal to the distance between the original pair.In the following figure, polygon before (left) and after (right) two sides are made equal distance from each other:

Radius Constraint

Constrains the radius to a user-specified value.

Equal Radius Constraint

Constrains selected radii to an equal length. In the following figure, two Circles before (left) and after (right) their radii are made equal:

Snapping

Snapping tools are used to snap the mouse to a specific point or edge in the EMPro geometry.

Snap to Grid Line

Mouse is snapped to the nearest point on the nearest grid line.

Snap to Grid Line Tool

Snap to Grid/Edge Intersections

Mouse is snapped to the nearest intersection between the grid and the sketch edge.

Snap to Grid/Edge Intersections Tool

Snap to Vertices

Mouse is snapped to the nearest vertex of the sketch or edge mid-point within range.

Snap to Vertices Tool

Snap to Edges

Mouse is snapped to the edges of a pre-defined object.

Snap to Edges Tool

Snap to Edge/Edge Intersections

Mouse is snapped to the vertices of intersecting edges.

Snap to Edge/Edge Intersection Tool

2-D Modeling Options

The 2-D Modeling tools are used to outline or fill-in a simple geometry object.

Wire Body

The Wire Body tool is the simplest geometry object. Any of the Shape tools can be used to create the desired wire geometry.

Sheet Body

The Sheet Body tool is similar to the Wire Body tool except its interior is filled with a material.

Sheet Body from Faces

The Sheet Body from Faces tool enables you to create a Sheet Body from the face of a pre-existing geometry object. The interface will prompt the user to select the desired object face.

3-D Solid Modeling Options

The 3-D Modeling tools are used to create simple solid geometry objects from 2-D forms.

Extrude

Extrude is used to sweep a face in the normal direction from its center. Once a 2-D form is made in the Edit Cross Section tab, select the Extrude tab to its right to perform an extrusion. For a default extrusion, define the distance in the Extrude Distance dialog box by typing in a numerical value, parameter name (See: Section Defining Parameters), or equation.

Additionally, the Direction dialog box specifies the axis along which the extrusion will occur. Clicking done after the desired geometry is created will add the object to the project. It can now be seen in the Project Tree.

Extrusion Tool

Revolve

Revolve is used to sweep a face in a circular path. Once a 2-D form in made in the Edit Cross Section tab, select the Revolve tab to perform a revolution. For a default revolution, define the angle in the Angle dialog box by typing in a numerical value, parameter name, or equation. The Axis Root Position dialog specifies the location of the root of the axis around which the shape will revolve. The Axis Direction box specifies the direction along which the revolution will occur. Clicking DONE after the desired geometry is created will add the object to the project. It can now be seen in the Project Tree.

Revolution Tool

Creating a sphere with the Revolution Tool

Advanced 3-D Solid Modeling Operations

The Advanced 3-D Modeling tools are used to modify a pre-defined 3-D geometry object. They are available within the Extrude and Revolve operations.

Twist

Twist options control how much the face is twisted as it is swept. They can be specified by angle or law.

By Angle: Specify the total number of degrees that the face will twist while it is swept.

By Law: Specify a mathematical expression to control the rate of twist as a function of the variable X .

In the following figure, the Twist Tool defined by A) Angle (90 degrees) and B) Law ( )

Draft Type

Draft Type options control the expansion or contraction of the edges of the face as it is swept from its initial position.

No Draft: No expansion or contraction of edges during sweep.
Draft Angle: Specify the expansion or contraction angle from initial position.

A cylinder sweep with Draft By Angle (10 degrees)

Draft Law: Specify a mathematical law to control the shape of the sides as the face is swept from initial position as a function of the variable X .

A cylinder sweep with Draft By Law (.5sin(2x))

End Distance/Start Distance: Specify the offset distance in the plane where the sweep ends/begins.

A cylinder sweep with Draft By End Distance (1 mm) and Start Distance (1 mm)

Hole Draft Type

Hole Draft Type options control the expansion and contraction of a hole. They are therefore only valid during sweeping operations applied to a faces that contain holes. Hole Draft Type can be defined based on the values assigned to the edges in Draft Type options, or by angle.

No Draft: No expansion or contraction is applied to the hole, even if the face has a Draft Type applied to it.

Draft Angle: Specify the expansion or contraction angle from initial position.

Hole with no Draft (left) and a defined Draft Angle (right)

With Periphery: The expansion or contraction of the hole will be the same as the outside edges of the face as specified in Draft Type.

Against Periphery: The expansion or contraction of the hole will be the opposite to the outside edges of the face as specified in Draft Type. (i.e., the hole will contract as the face expands and expand when the face contracts.)

Hole with Draft Angle against (left) and with the Periphery (right)

Gap Type Modeling Operations

The Gap Type specifies how to close the gap created by an offset. The default gap type is Natural, but the following options are available for filling gaps in the geometry.

Natural: Extends the two shapes along their natural curves until they intersect.
Rounded: Creates a rounded corner between the two shapes.
Extended: Draws two straight tangent lines from the ends of each shape until they intersect.

. Illustration of gap types, showing A) the original gap, B) Natural, C) Rounded and D) Extended.

Cut Off End

Controls the orientation of a face that does not follow its normal during a straight sweeping operation. Select this option to chop the end of the swept 3-D object so that the normal of the end face is aligned with the line used for sweeping. Original Model (Left) and Model After Cut Off End (Right)

Make Solid

This option makes the model entirely solid. If this option is not selected, the model will be hollow.

Modifying Existing Geometry

Specify Orientation

The Specify Orientation button is used to position the selected geometry in the simulation space. Clicking this icon will bring up the Specify Orientation tab.

Chamfer Edges

Chamfer Edges operation creates a beveled edge between two surfaces. After selecting the edge, it will be trimmed at a 45 angle if Constant Distance is selected in the Specify Distance tab. Otherwise, the user enters the chamfer distance for the surfaces on the left and right sides of the edge.

A Chamfer operation applied to a cylinder edge

Blend Edges

The Blend Edges operation rounds the selected edge of the geometry. Under the Specify Radius_tab, the user can enter the _Blend Radius to adjust the rounding factor.

A Blend operation applied to a cylinder edge

Shell Faces

The Shell Faces operation creates a shell from existing geometry. After selecting the faces to keep open, the user can enter the Shell Thickness under the Specify Thickness tab.

A Shell operation applied to a cylinder

Loft Faces

The Loft Faces operation connects two parts of an existing geometry. Under the Specify Loft tab, the user can adjust the Smoothness Factor to create the desired shape. In the following figure, two objects within a geometry with faces selected (left) and later connected by a Loft (right).

Remove Faces

The Remove Faces operation removes a blend or chamfer that was previously applied to a geometry edge. This operation must be applied before the user can offset the length of an object.

Offset Faces

With Offset Faces, the user enters a positive or negative offset distance to increase or decrease the length of the selected model, respectively. The following figure displays a cylinder with an applied negative offset (left) and positive offset (right).

Boolean Operations

Two Parts Boolean Operation

The Two Parts Boolean options perform operations on two existing geometry parts. In each case, one object is identified as the Tool (the part used to perform the modification), and the other as the Blank (the part that is modified). There are three types of operations:

• Subtract
• Intersect
• Union

In a Subtract operation, the Tool is subtracted from the Blank. In the Intersect and Union operations, the part selected first is inconsequential. The following figure displays the original two objects (Upper Left), objects after Boolean Union (Upper Right), objects after Boolean Intersection (Lower Left) and objects after Boolean Subtraction (Lower Right).

Extrude Boolean Operation

The Extrude Boolean option performs an operation on an existing geometry part. In this case, the user chooses the Blank, and then creates the object to use as the TOOL. The user then specifies the orientation of the extrusion and the nature of the operation (Subtract, Intersect, or Union). In essence, this operation is a shortcut for the Two Parts Boolean operation.

A boolean extrude operation

Revolve Boolean Operation

The Revolve Boolean option performs an operation on an existing geometry part. The user chooses the Blank, and then creates the object to use as the Tool. The user then specifies the orientation of the revolution and the nature of the operation (Subtract, Intersect, or Union).

A boolean revolve operation

3-D Patterns

Linear/Rectangular Pattern

The Linear/Rectangular Pattern option enables you to select a part in the geometry and replicate it in a linear pattern. After selecting the part to modify, define the Spacing and Number Of Instances in the U', V' and W' directions. Spacing refers to the distance between objects in the specified direction, and Number of Instances refers to the number of objects in the specified direction. For example, if three cylinders are to be spaced at 2-mm intervals in the U'-direction, the Spacing in the U'-direction is 2 mm and the Number of Instances in the U'-direction is 3. Additionally, the Stagger check-boxes apply a stagger in the specified direction at every other instance in that direction.

A linear pattern applied to a cylinder

Circular/Elliptical Pattern

The Circular/Elliptical Pattern option enables you to select a part in the geometry and replicate it in a circular or elliptical pattern. After selecting the part to modify, navigate to the Specify Circular/Elliptical Pattern tab and define the following fields:

• Axis Point - specifies the position of the axis
• Axis Normal - specifies values to define the direction of the pattern
• Root Position (available in Elliptical Mode) - specifies a point (usually the center of a part) to use as the reference to replicate in the elliptical pattern.
• Major Axis (available in Elliptical Mode) - specifies the direction of the major axis.
• Pattern Options
  • Instances - specifies the number of objects in the pattern
  • Angle - specifies the angle across which the objects are patterned (i.e., 180!img463.png! means that objects are patterned across half of the ellipse)
  • Ratio (available in Elliptical Mode) - specifies the ratio of the minor axis to the major axis

    An elliptical pattern applied to a small cylinder