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The One Way Clutch (see Figure 4.1) problem illustrates how a closed loop is used to find the variation of a kinematic assembly variable. Due to symmetry, only one vector loop is necessary to model the assembly. This assembly is designed to allow rotation in only one direction. The Hub is attached to a shaft, which in turn is attached to a driving mechanism. When the Hub rotates clockwise relative to the Ring, the spring is compressed and the Roller slips on the inside of the Ring. If the Hub rotates counter-clockwise, then the Roller wedges between the Hub and the Ring, causing the two to lock and rotate together.

Figure 4-1. One Way Clutch assembly.


Before beginning tolerance analysis, an accurate Pro/Engineer assembly drawing must be created containing all parts in their assembled positions. A representative drawing with dimensions and tolerances is given below in Figure 4-2. The assembly model must have the dimensions shown. The design variable of interest is the contact angle between the Roller and the Ring, [[phi]]1. Its nominal size is 172.9816[[ring]], and for the Clutch to work correctly, the angle must be between 172[[ring]] and 174[[ring]].

Assembly datum points must exist wherever a DRF, feature datum, joint, or specification endpoint is to be created. The assembly datum points must not be created as a group. Each must be done individually. Assembly datum planes or feature surfaces must exist to define the sliding planes for all joints other than revolute. For parallel cylinders joints, the sliding plane is tangent to the point of contact between the two cylinders. There must also be an assembly datum plane created to use as the 2-D reference plane. All assembly datum points must be created in this 2-D reference plane.

It is important to properly orient the parts within the assembly to prevent geometric error. All intersections should be true intersections or contact points can not be created correctly. Also, the drawing must be to scale or else errors will occur in reading the data. These errors will propagate throughout the analysis.

Figure 4-2. Dimensioned One Way Clutch.

For the remainder of this chapter, the following code will be used:

Select -- Select a menu option.

Pick -- Pick a point, plane, part, or modeling element on the drawing.

Enter -- Enter a value or name on the command line.


After an accurate assembly model of the Clutch (complete with assembly datum planes and points) has either been created or called up in Pro/Engineer, the TI/TOL 2D application can be run.


The first step in running the TI/TOL 2D application is to set the display. The Display option allows the user to define the plane in which the tolerance model will be built.

Pick An assembly reference plane (ADTM) that is parallel to the face of the Clutch by clicking on it with the mouse. The message window will prompt you for a plane that is perpendicular to the 2D reference plane.

Note: If an appropriate assembly datum plane has not been created, Done/Return out of TI/TOL 2D and create one. Re-enter as outlined above.

A reference plane for the TOL-2D commands has now been defined. The size of the tolerance symbols can also be modified with the Display option. The default size is 2.00.


A datum reference frame (DRF) must be established for each part of the Clutch assembly.

Creating the Hub DRF

We will now create the Hub DRF.

The message window will prompt you for a feature surface to establish the DRF direction. The DRF direction defines the angles at which vectors can enter and leave the DRF.

Creating the Ring DRF

The following steps will establish the DRF for the outer Ring of the assembly. The DATUMS, CREATE, and DRF TYPE menus should still be activated.

The cylindrical datum reference frame will be created and the cylindrical DRF symbol will appear at the center point of the Ring.

Note: If an assembly datum point has not been created in the correct location, Done/Return out of TI/TOL-2D and create it. Assembly datum points and planes cannot be created inside of TI/TOL-2D, but if the user exits TI/TOL-2D by means of Done/Return, the work on the model up to that point will be saved in the database. The user can create the required point or plane, re-enter TI/TOL-2D, and resume modeling where they left off.

Creating the Roller DRF

We will now step through the same procedure for creating the Roller DRF.

The cylindrical DRF symbol will appear at the center point of the Roller.

Note that the DRF's require an axis identification or a direction specification. Cylindrical DRF's automatically identify the longitudinal axis which is perpendicular to the cylinder's face. Rectangular DRF's, however, require the identification of a surface on the part which will establish the primary direction of the DRF.

DRF's have now been created for all three parts of the Clutch assembly. The assembly drawing should resemble Figure 4-3.

Figure 4-3. The One Way Clutch problem with DRF's defined.

If any DRF was created incorrectly, it must be deleted with the Delete command in the TOL-2D main menu.

Deleting a DRF

The incorrect DRF will be deleted and a new one can be created.

Modifying a DRF

A DRF may have its name and active degrees of freedom modified by the user. The name modification will be invisible in the modeler menus (for example when using Sel By Menu), but will be the node name seen when in the analyzer. Cylindrical DRF's may have their rotational degree of freedom turned off (or back on) in the modeler. The Clutch problem has a redundant rotational degree of freedom located at the Ring center. Both the Ring DRF and the revolute joint between the Ring and the Hub have a rotational degree of freedom, so one must be turned off. Therefore we will turn off the rotation of the Ring DRF.


Before joints can be created feature datums that define the paths from the joint location back to the DRF's of both parts associated with the joint must be created first. In the Clutch problem a rectangular feature datum is required to provide a vertical path from the Hub DRF to the surface of the Hub. An assembly datum point should already have been created in the Pro/Engineer modeler at this location.

The feature datum will be created and will be identified with a square-box symbol at the specified location (See Figure 4.4).

Select Done Sel from the GET SELECT pop up menu.

All of the feature datums for the Clutch assembly have now been created. If the feature datum was created incorrectly, it can be deleted the same as a DRF. Feature datums can also have their names and active degrees of freedom modified in the same manner as outlined for DRF's.

Figure 4-4. The One Way Clutch with feature datums defined.


The next step in the TI/TOL 2D analysis is to locate the contact joints between each part. These joints represent the kinematic constraints between mating parts. The DRF's and feature datums created previously will be used to locate the joints by tracing a path back to the respective part DRF through controlled and dependent dimensions. The following steps will outline how to create the three kinematic joints required for the Clutch assembly.

Creating the Revolute Joint Between the Hub and Ring

The first contact joint which connects the Hub to the Ring will be created and the revolute joint symbol will appear at the specified location.

Note: If Sel By Menu is used to select the part DRF's, the Done Sel option on that same menu must be used after each DRF selection to complete the sequence.

Creating the Cylindrical Slider Joint Between the Roller and Hub

Creating the Parallel Cylinders Joint Between the Roller and Ring

All of the contact points necessary to create loops have been added to the drawing (see Figure 4-5 below). If a joint was created incorrectly, the Delete command in the TOL-2D main menu can be used to delete the incorrect joint. The procedure is identical to deleting a DRF. The joint can then be created correctly before continuing with the tolerance modeling.


Figure 4-5. Joints for One Way Clutch.

Modifying Joints

A joint may have its name and active degrees of freedom modified by the user. The name modification will be invisible in the modeler menus (for example when using Sel By Menu), but will be the node name seen when in the analyzer. No degrees of freedom will be changed on the joints, but the name of the revolute joint will be changed to Phi2.


Joint degrees of freedom are modified in the same manner as datum degrees of freedom.


The next step in the modeling process is to create the kinematic loops which relate all assembly parts and contact joints to the resultant assembly dimensions. Although the Specification command in the TOL-2D main menu precedes the Loops command, closed loops must be created before closed loop specifications (dependent lengths and angles) can be applied. However, open loop specifications should be created before loops are generated. The Clutch requires one closed loop.

Creating Loops

The loop we will create will relate the three joints in the assembly.

The Autoloop command will automatically create the kinematic loop that relates the joints and datums in the assembly. The loop should appear as in Figure 4-6.

Figure 4-6. One Way Clutch with loop defined.

Deleting Loops

Loops can be deleted by following the same procedure as for deleting part DRF's. If there are one or more closed loop specifications applied to a closed loop, those specifications must be deleted before the modeler will allow that closed loop to be deleted. Open loops have no such restrictions.


Loop vectors can be modified in three ways. The user can change the vector names and vector tolerances. They can also equivalence vectors for cases when the variations of two vectors are not independent of each other. For example, if the radius of a cylinder is over-sized at one point, it is likely to be over-sized at all other points.

Modifying Vector Names

The user can apply new names to the loop vectors. These new names will remain invisible until the user enters the Analyzer.

Modifying Vector Tolerances

Each vector that corresponds to a manufactured dimension must have a tolerance associated with it. Vectors that represent kinematic assembly dimension (closure lengths, such as the vector between the feature datum and the cylindrical slider joint) should not be assigned a tolerance.

Equivalencing Two Vectors

The variations of radii of the Roller are not independent of each other. They will be equivalenced in order to link their variances in the tolerance model.


Design specifications may now be included in the TI/TOL 2D model to define acceptable variations for critical assembly dimensions.

Creating a Dependent Angle Specification

The specification in this problem will be applied to the dependent angle formed by the contact between the Roller and the Ring (see Figure 4-7).

The dependent angle specification will be applied and the dependent angle tolerance symbol shown in Figure 4-7 will appear inside the specified dependent angle. Again, an incorrect design specification can be deleted by using the Delete command in the TOL-2D main menu.

Figure 4-7. Dependent Angle Specification.

Modifying Design Specifications

The acceptable variation limits of design specifications can be modified after the design specification has been created. If the specification limits applied to the dependent angle are entered wrong, they can be corrected as outlined below.


TI/TOL 2D includes geometric tolerancing options. Geometric tolerances allow an engineer to account for machined surface variations such as flatness, circularity and perpendicularity. These surface variations can accumulate and propagate kinematically through the model the same as dimensional variations.

Applying a Flatness Tolerance to the Hub

The first geometric tolerance to be applied will be a flatness on the Hub.

The flatness tolerance will be applied to the specified joint and the flatness tolerance symbol will appear at the joint.

Applying a Circularity Tolerance to the Roller

We will now apply a circularity tolerance to the Roller at both joints associated with the Roller.

The specified circular tolerances will be created and the circular tolerance symbols will appear at the joints. The tolerance symbols will be placed on top of the symbols that are already at the specified joints.

Applying a Circularity Tolerance to the Ring

We will now apply a circularity tolerance to the Ring.

Applying a Concentricity Tolerance to the Ring

The final geometric tolerance is a concentricity tolerance applied to the Ring.

The concentricity tolerance will be applied at the specified location. Any incorrect geometric tolerance can be deleted by deleting its geometric tolerance symbol.

Modify Geometric Tolerances

The user has the option of modifying the bandwidth of any previously applied geometric tolerance.

The Clutch assembly will now appear as shown in Figure 4-8.

Figure 4-8. Clutch assembly with geometric tolerances applied.


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