# Mecanica

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Planetary Gear Train Working Model Tutorial 2

1

Objectives
• In this tutorial you will learn to: • • • •

Create pin joints and rigid joints Use the Gear tool Assemble mechanisms that lie in parallel planes Use conditional statements Use chain drives and friction belts

Design Principles related to this tutorial
• • • •

Compound gear trains Epicyclic or planetary gear trainsGear ratios Gear trains with more than one degree of freedom Chain drives and friction belts

INTRODUCTION Problem Statement
Gear trains, chain drives, and friction belts are used in virtually every type of engineering application for transmitting rotational motion from one shaft to another. The ratio of output to input rotational speed is determined by the number of gears, their geometricarrangement, and their relative sizes. In this tutorial you will use Working Model gears to create a gear train; you will then examine how that gear train could be operated for several different applications. Figure 1 shows a schematic drawing of the top and side views of the pitch circles for a gear train composed of four spur gears. Pitch circles are imaginary circles that roll together as if thegears were friction wheels. The pitch circle radii are as follows: r1 = 0.5 m, r2 = 0.8 m, r3 = 0.2 m, r 4 = 1.5 m. Gear 4 is an internal gear. The arm, labeled object 5, is 1.3 m tall and 0.1 m wide. Gears 2 and 3 are rigidly keyed to the same shaft and rotate together. Gears 1 and 4 are attached to independent shafts. The gear train operates in a horizontal plane. Create a Working Modelsimulation of this gear train and examine the relative speed ratios of the gears for three cases: 1. The arm is fixed and gear 4 is driven at a constant speed of 30 rpm clockwise. 2. Gear I is fixed and gear 4 is driven at a constant speed of 30 rpm clockwise. 3. None of the objects is fixed, gear 4 is driven at a constant speed of 30 rpm clockwise, and arm 5 is driven at a constant speed of 10 rpmcounterclockwise.

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Figure 1

Setting Up the Workspace
Open a new Working Model window with the workspace settings you have used in each tutorial. • Be sure your simulation is using Accurate mode. The gears operate in a horizontal plane; there- fore there will be no acceleration due to gravity in this problem. • • Use the Gravity dialog box to set Gravity to None.

You will want to enter andview gear velocities in rad/s, so you will change the units now. Use the Numbers and Units dialog box to change the Units Systems to SI (radians).

Creating the Components
You will now create and label the gears and arm. Since this is a fairly complicated mechanism, create the elements in the order in which they are numbered in Figure 13.1 and described in the Problem Statement, and assemblethem exactly as instructed in this tutorial. The Working Model mass numbers will then be the same as the labels in Figure 13.1 and will correspond with the mass numbers given in the tutorial, so you will be able to check your work. • • Create four circles to the side of your work- space. Create one rectangle to the side of your workspace.

Your workspace should look like Figure 2.

Figure 2

3 You will now begin to position and size the objects in your workspace. You must use the Properties window for the exact placement of every object in this tutorial. This is very important for smooth operation of the gears; you will not be able to run the simulation if you are not precise in the placement of all objects. • • • • • Open the Geometry, Properties, and Appearance windows. Make theradius of Mass [l] equal to 0.5 m, and place its center at (0,0). Make the radius of Mass [2] equal to 0.8 m, and place its center at (0,1.3). Make the radius of Mass [3] equal to 0.2 m, and place its center at (0,1.3). Label all five objects according to the Problem Statement, in the order in which they were created.

Tip You can include spaces in front of the label you type in the Appearance...