# Parametric Design of a Shaft Assembly

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Parametric design is a process based on algorithmic thinking that enables the expression of parameters and rules that, together, define, encode and clarify the relationship between design intent and design response.

Parametric design is a paradigm in design where the relationship between elements is used to manipulate and inform the design of complex geometries and structures.

Grasshopper is a visual programming language and environment that runs within the Rhinoceros 3D computer-aided design (CAD) application.

## Step 1: The Original Problem

The original problem is to be found in the Shigley’s Mechanical Engineering 10th edition problem 3.73.

In the main problem The Principal Stress are to be found. But in my study the goal is to find the rod’s diameter.

## Step 2: IDEF Diagrams Generation

After specifying the input parameters, the required mechanisms and constant parameters are set. The required results are also to be set. IDEF diagrams are used to help set these parameters.

The IDEF process starts with the main block which is the "Create Shaft Assembly". Then this block is exploded into the main step functions of the process.

## Step 3: Parametric Problem Generation

1.The solution of the program is initiated by entering the parameters. Also, setting the constant parameters are required.

2.After that, the program is to calculate the reaction forces at the pillow blocks.

3.From the reaction forces, the moments at each gear are calculated.

4.The diameter is then found by dividing to the maximum moment.

## Step 4: The Control Parameters

First of all we need to specify the parameters that we want to control

•The Two Forces Magnitudes.

•The Forces Locations.

•The Length of the rod.

•The Gears Diameters.

•The Yield Strength.

•The Safety Factor.

Slider blocks are generated to represent these parameters accordingly.

Torque is also needed to be calculated initially.

## Step 5: Calculating the Reaction Forces

The following parametric equations are used to calculate the Reaction Forces.

Grasshopper blocks are generated accordingly.

## Step 6: Calculating the Moments

The following parametric equations are used to calculate the Moments.

Grasshopper blocks are generated accordingly.

## Step 7: Calculating the Diameter

The following parametric equations are used to calculate the diameter.

Grasshopper blocks are generated accordingly.

## Step 8: Visualization Blocks

These visualization blocks use the dimensional values of of the gears, pillow blocks and shaft to generate the CAD drawing representation of the assembly.

## Step 9: Rendering Results

The CAD results are rendered in the Rhino program interface.

## Step 10: The Full Canvas of the Grasshopper Interface

This is the full canvas of the Rhino 3D grasshopper interface.

## Step 11: Further Results

These results can be saved as an .dwg extension to be opened in the Autocad and used for manufacturing purposes.