PART MODELING ASSIGNMENT 7: Plane and Space Curves

Objective: The aim of this assignment is to create some plane and space curves and use them to make parts

PART I Helical Spring Helix is a common space curve, which has many engineering applications, E.g. instance, helical spring, staircase etc.

Figure 1: Helical spring Procedure: 1. Generating a helix: Using function spline we create a helix with details as given in figure 2. Recall the parametric equation of a helix. x = r cos(u); y = r sin(u) z = bu , where u is the parameter, r is the radius and b is a constant that gives the longitudinal spacing between the turns.

Figure 2: Algebraic Equation Editor of Function Spline and its result

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2. Now we create a helical solid using Sweep command. The helix created in the previous step will be used as the Path Curve in this procedure. Draw a circle of 5mm radius as the Cross Sectional curve for creating this solid

Figure 3: The Sweep command with its result

Exercise 7a: Spiral of Archimedes Model a spiral shaped spring as shown in figure 4 below. Take the cross section as a circle of 5mm diameter and the spring should have about 6 turns. Write downs the parametric equations used to generate this object. Hint: What changes in the (parametric) equation of helix will give you a spiral?

Figure 4: Archimedean Spiral and spring

2 Exercise 7b: Battery Spring A metallic battery spring holds the battery in place and also connects the electrode to the circuit. Usually it is in the form of a conical helix as shown in figure 5 below. Model a spring of the above description with a circular cross section of 5mm diameter and having about 6 turns. Hint: Now we combine the features of spiral and helix together

Figure 5: Spring in the shape of conical helix

Exercise 7c: In and Out Curve A curve created by starting with a circle, dividing it into six equal arcs, and flipping three alternating arcs. The process could then be repeated an infinite number of times. These curves are useful in designing parts like cams, timer gears, rotating lobes etc. Create the following in and out curve starting from a circle of radius 50mm.

Figure 6: The in a nd out curve

3 Hint: The solution is shown for n=4, extend it to n=6

Figure 7: The in and out curv e for n=4 (divisions)

Figure 8: Starting step for an i n and out curve with n=6

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