## 1.2 ASSEMBLY AND KINEMATICS

• It is difficult for the computer to distinguish between two or more parts, and how they are related

• Assemblies tend to have a hierarchy of sub-assemblies and parts

• Another important concept is an instance. For example, a bolt is a single part in a CAD system, but there may be 10 instances of the bolt in a product.

• Each instance of a part has,

- a position

- an orientation

- a unique identification

- other information the designer chooses to associate

• It is also important to define instances in an assembly as a chain of kinematic entities. Some common joints are,

- slider

- rotary

- spherical

- universal

- ground (a special case for kinematic solutions)

• Assembly planning requires some representation of a precedence for assembly mating. The example that follows shows some of the data structures which may be used for describing an assembly.

### 1.2.1 Tolerancing

• The real value of tolerancing becomes obvious when we begin to consider assemblies.

• The obvious methods of tolerancing are,

- dimensional tolerancing

- geometrical tolerancing

• There are many methods for dealing with tolerances when working by hand (eg. Maximum metal condition)

• The trade off to be handled by tolerancing is tighter tolerances increase quality, but they slow production, and increase cost.

• As tolerances are stacked up, accumulated errors occur. It is hard to predict what effects these errors will have.

• The ability to obtain a tolerance can also be effected by the manufacturing method chosen.

• A popular computer based method for tolerance analysis is the Monte Carlo simulation. In effect, each tolerance has a random distribution, and it is varied randomly. The effect is noted, and statistics are gathered from the model. The basic process is outlined below.

• Monte Carlo Tolerance Evaluation,

1. Generate a candidate instance of an as-manufactured part using a normal (or other) distribution random number generator to perturb the vertices of the part within the specified size tolerance zone.

2. Check if the part instance meets the specified form tolerances. This is needed because form tolerances may be tighter than size tolerances, and because normal distribution may, in rare cases, generate perturbations with standard deviations beyond the size tolerance zone.

3. If one or more of the vertices of the part instance are found out of zones of form tolerances, the part instance is rejected. If all vertices are inside the zone, the part instance may be accepted.

4. Repeat steps 1 to 3 for all other parts in the assembly.

5. Use the solid modeler to create the assembly instance using all the instances created in step 4. These instances are positioned relative to datums established by part features.

6. Check if the assembly instance from step 5 satisfies the design constraints. If yes, the assembly is accepted. If not, the assembly is rejected.

7. Repeat steps 1 to 6 as many times as the desired sample size (number of assembly instances) is used to calculate the statistics. The larger the sample size the better, and the more confidence we have in the results.