NORMAL AND TANGENTIAL COMPONENTS (Section 12.7) When a particle moves along a curved path, it is sometimes convenient to describe its motion using coordinates other than Cartesian. When the path of motion is known, normal (n) and tangential (t) coordinates are often used. In the n-t coordinate system, the origin is located on the particle.

This functionality is available on Onshape's browser, iOS, and Android platforms.

Mates in Onshape are different than mates in old CAD systems. There is only one Onshape Mate between any two instances, and the movement (degrees of freedom) between those two instances is embedded in the Mate. Mates contain their own coordinate systems, so you ever only need to use one Mate to define the degrees of freedom between two entities. At the time of placing a mate between two entities, Onshape will offer points on each entity to which to align with the mate's coordinate system. The suggested locations are based on the underlying geometry of the part and changing the geometry will change the location of the mate. This can be undesirable in certain situations, but you can also:

• Tangential point definition: a point at which a geometric line, curve, plane, or curved surface touches another. Meaning, pronunciation, translations and examples.
• Slot- averaged and cylinder- averaged value. Dynamic variations in slot velocity will be studied herein, but this is done in support of increasing the overall time- averaged velocity. Likewise the consideration of spatial variations of slot velocity across the width of the slot will be made to elucidate the factors underlying screen capacity.
• Traditional slot milling cutters require two different shapes of inserts in pairs, using one shape for the right corner and the other for the left, in order to complete the slot profile. Both TungUniversalSlot and TecTangentialSlot incorporate a double-sided insert, allowing one side to be used for the right hand and the other for the left hand.

• Add an explicit mate connector to an entity exactly where you want it if the geometry does not already allow an implicit mate connector while creating a mate. For more information, see Mate Connector.
• Insert a layout or reference sketch in an Assembly to use for aligning mate connectors.

Shortcut: m

Use the shortcut key j to hide/show mates in an assembly.

Note that you are able to mate entities to the Origin in an Assembly. You are also able to Fix an entity in order to test the movement of assigned Mates using the context menu or drag.
Entities include: parts, assemblies, subassemblies, sketches, and surfaces.

Mate dialog

Mates are defined through the Mate dialog:

You select the type of mate to create, then select the mate connectors (one for each part). You are also able to check the box to apply limits of movement. Other options/action include:

• - Flip the primary axis, Z orientation, of the instances.
• - Reorient the secondary axis; rotate the quadrant orientation (in the XY plane) of the instances by 90 degrees at a click.
• - Preview the animation of unlimited movement of the mate, ignoring all other mates in the assembly.
• Solve - Solve all assembly mates including this one.

Many mates offer the ability to set an Offset distance for defining a fixed space between the parts being mated, as well as distance Limits for movement.

Limits are visualized in the graphics area as dashed lines with bars at the ends. The dashed lines represent the direction and distance of the movement and the solid lines represent the limit.

Offset distances are visualized in the graphics area as dashed lines between the Mates, displaying the value and the axis. Enter the distance in the dialog.

When you click on a Mate, graphics are displayed to indicate the direction of the X, Y, and Z as defined by the Mate along the with the offset and the range of limits dimensions (if any).

Applying an offset should be viewed as moving the entire coordinate system. The offset is relative to the Mate connector selected first.

When the Offset box is checked, many mates also offer an option to specify rotation about a specific axis: Slider, Revolute, Pin Slot, Planar, and Fastened mates include the option, as see below:

Select the axis about which to rotate, above, then enter the degrees of rotation

When you open a Mate dialog and select two Mate connectors, a head-up display appears at your cursor:

Click the checkmark in the head-up display to commit the current mate and start a new Mate. The Mate dialog box stays open, and you are free to continue selecting Mates.

Offset distances are visualized in the graphics area as dashed lines between the Mates, with editable values. Drag the part to a desired position, double-click the distance value and enter a new value. These values are not persisted; you are able to use them to estimate values to enter in the Offset field in the dialog, or place parts in precise positions in order to take measurements. For example:

Mate values for axes and rotational movement (above).

Mate value in edit (above).

Mate context menu

Use the Mate context menu to access the following commands:

• Rename - Specify a different name for the Mate
• Edit... - Change the Mate definition
• Reset - After an assembly is dragged to test movement of Mates, use Reset to return the assembly to its starting/home position (assuming constraints don't restrict that)
• Animate - Drive the assembly from a single Mate (or single DOF within a mate)
• Hide - Remove from view (Show displays the Mate again)
• Show all mates - Show all Mate connectors
• Isolate - Dim and inactivate all other parts except those selected (or associated with a selected Mate). When in Isolate mode, Exit isolate appears at the top of this menu. For more information, see Managing Assemblies.
• Make transparent - Dim parts nearest to the mate selected. Use the slider on the Make transparent dialog to extend the transparency out to other parts either by distance from, or by connectivity to, the selected mate.
• Suppress - Visualize the assembly without the Mate (and without deleting the Mate)
• Clear selection - Clear all selections
• Delete - Remove the Mate from the assembly

Reordering mate features

Once a Mate is created and listed in the Mate Features list, select a Mate (or Ctrl-click to select more than one) and drag/drop to reorder them in the list. This will help put the most important mate features higher and more visible in the list. Onshape solves mates simultaneously so order won't affect a Mate.

You have the ability to specify Mate values of all mates except Ball, Fastened, and Tangent. Onshape provides visual cues for distances, and provides distance values, in default units, from the second Mate connector selected to the first. Specify limits in positive and negative values.

In this example, the Mate connector on the box was the first one selected in the dialog; the Mate connector on the cylinder was the second selected. Notice that the Y value is negative and the X value is positive.

Now, switch the order of Mate connector selection and notice the distance values:

Notice that in this scenario, the Y value is positive and the X value is positive. This is due to the order of measurement from one Mate connector to the other. It's important to remember that the measurement is made from the second selected Mate connector to the first, along the coordinate system.

Use these distance visualizations to estimate the value to enter in the Limits box:

1. When the Limits check box is present for a Mate, click to enable degrees of freedom fields to enter values for the minimum and maximum distances, as measured from the second Mate connector selected, to the first selected.
2. Using the distance visualization as a guide (drag the part to activate), enter a minimum and maximum value.
3. Use the Play button to animate the movement, including limits.

You are able to use expressions and trigonometric functions in numeric fields in Assemblies.

Use the Animate command (found in the context menu for mates and mate indicators) to drive the assembly from a single Mate (or single DOF within a Mate). Other Mates and relations in the assembly are also enforced and honored.

If you have defined limits for the Mate, those values are used as the start and stop points during the animation.

1. Right-click on a mate or mate indicator and select Animate.
2. Animate works with only one degree of freedom at a time, so if the Mate has more than one, you are prompted to select one.
3. Enter Start and End values. If Limits are specified in the Mate definition, those values are automatically populated in the Start value and End value fields. If no Limits are specified in the Mate dialog, enter values now.
   1. Start value - The minimum distance measured along the degree of freedom’s axis. (By default, the value as specified in the Mate Minimum Limit.)
   2. End value - The maximum distance measured along the degree of freedom’s axis. (By default, the value as specified in the Mate Maximum Limit.)

      Note that you are able to enter up to 36000 degrees here (100 revolutions), specifically helpful for visualizing degrees of freedom in high-ratio gears and rack and pinion relations.

4. Specify Steps, a linear map from the start to end value, inclusive, interpolated at each step. The minimum number of steps is 2. By default, playback is around 60 steps/second.
5. Select a playback type, Single or Reciprocate to play the animation of the degrees of freedom once or continuously until you manually stop it, respectively.

Current value is a read-only field and is populated during animation as the Mate moves through the degrees of freedom, in your specified units. When the motion stops (either automatically or manually), Current value displays the point at which the motion was stopped.

Animate supports all Mate types but it’s not recommended to use Fastened, Tangent, or Ball as the driving mate.

Tips

• The Animate command works with various graphics modes, like Isolate, Mate indicators and Mate connectors.
• Animate helps you explore the relationships between Mates, their constraint systems, and gives you a way to show off your design (especially with the playback loop feature, specifically for rotational degrees of freedom).

Offset entities during assembly

Offsetting entities from one another during assembly is available for the following Mate types:

• Planar offset - Along the Z axis
• Slider offset - Along the X and Y axes
• Revolute offset - Along the Z axis
• Pin slot offset - Along the Z axis
• Fastened offset - Along the X, Y, and Z axes

You are also able to drag the entities and observe the distance values in the graphics area. These will help determine the specific values to enter in the dialog.

You are able to use expressions and trigonometric functions in numeric fields in Assemblies.

Copying/Pasting assembled entities

You are able to copy and paste entities that have been mated in an Assembly:

1. Select the entities.
2. From the context menu, select Copy items:
3. From the context-menu, paste the items:

The entities are pasted directly where the mouse click occurs.

Notice that the entities, mate connectors, and mates are also duplicated in the Assembly list.

Mate indicators

In addition to being visible in the Assembly list, mates have indicators in the graphics area as well. You have the ability to hide the entities and mate connectors in the Assembly list in order to see these mate indicators more clearly. These indicators give hints at the type of motion they define as well as the current state: blue/white indicates good Mates, gray indicates suppressed or inactive, and red indicates a problem:

Fastened

Revolute

Slider

Planar

Cylindrical

Pin slot, with an arrow in the direction of the slot

Ball

Tangent

Parallel

Group

More tips for visualizing Mates:

• Select a part, right-click for the context menu and select Show mates.
• Hover over a Mate, right-click for the context menu where you are able to take action on the Mate.
• Select a Mate, Mate connector, or Mate relation in the graphics area and its associated instances and Mate feature are highlighted in the list.

Concepts

• There is exactly one Mate between any two instances.
• Fixing an entity is different from applying a Mate. Fix (found in the context menu) is specific to the assembly in which it is applied; it does not carry over to any other assembly that entity is inserted into.
• The Mate positions two instances in relationship to each other, aligning a Mate connector on each instance.

  Before Mate

  After Mate

• The initial position is often a best guess. There are two tools to correct the position:
• The Flip primary axis tool flips the major (Z) orientation.
• The Reorient secondary axis tool adjusts the orientation in 90 degree increments
• The play button animates the allowed movement between the Mate being created.
• The Solve button regenerates the mate in process and the movement of all Mates, so you have the ability to see how your changes affect the entire assembly.

The Mate type then specifies the degrees of freedom behavior.

Example

1. Select a Mate (for example ) to open the dialog:
2. Select one automatic Mate connector on each entity (you can also Mate to the Origin):
3. If necessary, adjust the orientation using Flip Primary Axis or Rotate Secondary Axes.
4. Accept the Mate .

In the example above, only automatic Mate connectors were used. In most mating cases, automatic Mate connectors will work fine. In some less common cases, it may be useful to create Mate connectors ahead of time. You have the ability to create Mate connectors in either the Assembly or in the Part Studio.

Mates: iOS

Mates in Onshape are different than mates in traditional CAD systems. There is only one Onshape Mate between any two instances, and the movement (degrees of freedom) between those two instances is embedded in the Mate.

Note that you are able to mate an entity to the Origin in an Assembly. You are also able to Fix an entity, in order to test the movement of assigned Mates, using the context menu. Entities include: parts, assemblies, subassemblies, sketches, and surfaces.

Mate dialog

Mates are defined through the Mate dialog:

Select the type of Mate to create, then select the Mate connectors (one for each part).

Mate type - The Mate type field displays the type of Mate you are using. Tap to open a list of Mate types and tap to select one.

Mate connectors - The next section, Mate connectors, is highlighted in blue. This indicates that a selection from the graphics area is required. Two Mate connectors (one from each instance being mated) must be selected.

Offset - Tap to set an offset distance for defining a fixed space between the parts being mated.

Limits - Tap to set distance limits for movement.

- Flip the primary axis, Z orientation of the instances.

- Reorient the secondary axis; rotate the quadrant orientation (in the XY plane) of the instances by 90 degrees at a tap.

Solve - Tap to solve all assembly Mates including the current one.

You have the ability to specify movement limits of all Mates except Ball, Fastened, and Tangent.

Inside the dialog of a Mate that allows limits (Revolute, Slider, Planar, Cylindrical, and Pin slot) toggle the Limits button on and limit fields appear.

Enter desired limit specifications and tap Solve to visualize the changes.

Offset entities during assembly

Offsetting entities from one another during assembly is available for the following Mate types:

• Planar offset - Along the Z axis
• Slider offset - Along the X and Y axes
• Revolute offset - Along the Z axis
• Pin slot offset - Along the Z axis
• Fastened offset - Along the X,Y, and Z axes

You are also able to drag the entities and observe the distance values in the graphics area. These will help determine the specific values to enter in the dialog.

You are able to use expressions and trigonometric functions in numeric fields in Assemblies.

Mate indicators

In addition to being visible in the Assembly list, Mates have indicators in the graphics area as well. You are able to hide the entities and Mate connectors in the Assembly list in order to see these Mate indicators more clearly. These indicators give hints at the type of motion they define as well as the current state: blue/white indicates good Mates, gray indicates suppressed or inactive, and red indicates a problem.

Fastened

Revolute

Purpose Of Tangential Slots Machines

Slider

Planar

Cylindrical

Pin slot, with an arrow in the direction of the slot

Ball

Tangent

Parallel

Group

More tips for visualizing Mates:

• Two-finger tap for the context menu, tap Show all to show everything listed in the Instance list, including Mate connectors and Mate indicators.
• Tap on a Mate in the Instance list.

Concepts

• There is exactly one Mate between any two instances.
• Fixing an entity is different from applying a Mate. Fix (found in the context menu) is specific to the assembly in which it is applied; it does not carry over to any other assembly that entity is inserted into.
• The Mate positions two part instances in relationship to each other, aligning a Mate connector on each instance.

  Before Mate

  After Mate

• The initial position is often a best guess. There are two tools to correct the position:

The Flip primary axis tool flips the major (Z) orientation.

The Reorient secondary axis tool adjusts the orientation in 90 degree increments.

• The Solve button regenerates the mate in process and the movement of all Mates, so you have the ability to see how your changes affect the entire assembly.

The Mate type specifies the movement behavior.

Mates: Android

Mates in Onshape are different than mates in traditional CAD systems. There is only one Onshape Mate between any two instances, and the movement (degrees of freedom) between those two instances is embedded in the Mate.

Note that you are able to mate an entity to the Origin in an Assembly. You are also able to Fix an entity, in order to test the movement of assigned Mates, using the context menu. Entities include: parts, assemblies, subassemblies, sketches, and surfaces.

Mate dialog

Mates are defined through the Mate dialog:

Select the type of Mate to create, then select the Mate connectors, inferred or existing (one for each part).

Mate type - The Mate type field displays the type of Mate you are using. Tap to open a list of Mate types and tap to select one.

Mate connectors - The next section, Mate connectors, is highlighted in blue. This indicates that a selection from the graphics area is required. Two Mate connectors (one from each instance being mated) must be selected.

Offset - Tap to set an offset distance for defining a fixed space between the parts being mated.

Limits - Tap to set distance limits for movement.

- Flip the primary axis, Z orientation of the instances.

- Reorient the secondary axis; rotate the quadrant orientation (in the XY plane) of the instances by 90 degrees at a tap.

Solve - Tap to solve all assembly Mates including the current one.

You are able to specify movement limits of all Mates except Ball, Fastened, and Tangent.

Inside the dialog of a Mate that allows limits (Revolute, Slider, Planar, Cylindrical, and Pin slot) toggle the Limits button on and limit fields appear.

Enter desired limit specifications and tap Solve to visualize the changes.

Offset entities during assembly

Offsetting entities from one another during assembly is available for the following Mate types:

• Planar offset - Along the Z axis
• Slider offset - Along the X and Y axes
• Revolute offset - Along the Z axis
• Pin slot offset - Along the Z axis
• Fastened offset - Along the X,Y, and Z axes

You are also able to drag the entities and observe the distance values in the graphics area. These will help determine the specific values to enter in the dialog.

You are able to use expressions and trigonometric functions in numeric fields in Assemblies.

Mate indicators

In addition to being visible in the Assembly list, Mates have indicators in the graphics area as well. You have the ability to hide the entities and Mate connectors in the Assembly list in order to see these Mate indicators more clearly. These indicators give hints at the type of motion they define as well as the current state: blue/white indicates good Mates, gray indicates suppressed or inactive, and red indicates a problem.

Fastened

Revolute

Slider

Planar

Cylindrical

Pin slot, with an arrow in the direction of the slot

Ball

Purpose Of Tangential Slots Games

Tangent

Parallel

Group

Purpose Of Tangential Slots Machine

More tips for visualizing Mates:

• Two-finger tap for the context menu, tap Show all to show everything listed in the Instance list, including Mate connectors and Mate indicators.
• Tap on a Mate in the Instance list.

Concepts

• There is exactly one Mate between any two instances.
• Fixing an entity is different from applying a Mate. Fix (found in the context menu) is specific to the assembly in which it is applied; it does not carry over to any other assembly that entity is inserted into.
• The Mate positions two part instances in relationship to each other, aligning a Mate connector on each instance.

  Before Mate

  After Mate

• The initial position is often a best guess. There are two tools to correct the position:

The Flip primary axis tool flips the major (Z) orientation.

The Reorient secondary axis tool adjusts the orientation in 90 degree increments.

• The Solve button regenerates the Mate in process and the movement of all Mates, so you have the ability to see how your changes affect the entire assembly.

The Mate type specifies the movement behavior.

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Last Updated: December 10, 2020

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