ME-461 Date: 28/01/2011

Assignment No.#1 Submission date:09/02/2011

1. A point A (4, 56,3) is scaled by factor 5 with respect to origin. Find the new coordinates of the

scaled point. Why scaling is different from translation? Give an example.

2. Rotate a point A(1,2) in 2D with respect to the origin by 36 counterclockwise, and find

coordinates of the rotated point.

3. Rotate a point A(1,2) with respect to point B (3,4) for the same angle, and find the coordinates

of the rotated point.

4. Rotate a point V(2,3,4) in 3D with respect to a point W(8,5,6) by 45 counterclockwise, and find

the coordinates of the rotated point.

5. The two end point of a line are (3,2,6) and (1,4,7). First line is rotated by 47 counterclockwise

with respect to a line defined by points (9,3,15) and (4,3,9). Then it is scaled by a factor of 3 with

respect to the origin. Find the coordinates of the endpoints of the transformed line.

6. Consider an object shown in Fig 1. Perform the following transformations if the coordinates of

the vertices of the object are A(1,12), B(13,2),C(19,2),D(19,8),and E(13,12).

Fig.1: showing object

7. Scale the object such that the edges are increased by a factor of 4.Rotate the object about point

A by 45 in the counterclockwise direction.

8. Prove that two successive 2D transformations are additive: T (d1) T (d2) = T (d1+d2). Is this also

valid in 3D case?

9. Every transformation discussed in class is a special case of the general linear transformation

given by:

X=m1.x+n1.y+l1

Y=m2.x +n2.y +l2

Specify the range of parameters m1, n1, l1, m2, n2 and l2 that define the transformation discussed

in the class.

10. Drive the parametric equation for (x-a) 2+(y-b) 2= r2.

11. Two end points of a curve segment are A(2,3) and B(4,6) and the slopes at these two points are

45 and 75,respectively with magnitude 4. Develop the Hermite curve equation and draw the

curve.

12. Suppose the end point of another curve segment is A(7,9) and the slope is 35. Develop a curve

that is connected to the curve in above problem with C1 continuity.

13. Give four control points A(4,8),B(7,9),C(8,1) and D(10,4) ,develop the cubic Bezier curve

equation and draw the curve.

14. Repeat the above problem with respect to a quadratic B-spline surface.

15. A company wants to manufacture a part requiring a drilling operation. The hole is to be drilled

to dimensions 2 0.002 in. Company has decided to use your service as a concurrent engineering

consultant. Help the company, develop the design of the part and select the appropriate

manufacturing process if 10,000 parts are delivered. The company has gathered the following

data:

Raw material cost per unit= $ 2.00

Salvage value per unit = $ 0.50

Other data are given below in table:

16. A system consisting of a gear and pulley assembly on a shaft is used to transmit power as

suggested by Enrick (1985). The assembly system arrangement consists of spacer, gear, spacer,

pulley and then spacer. The spacers are produced on an automated punch press with a process

standard deviation of 0.0005 in. at a cost of $0.75 each. There are a number of alternatives for

manufacturing the gear and pulley. The following data are available (standard deviation is

expressed in inches):

There is stacking of tolerances for the system elements. However, the assembly tolerance must

not exceed 0.011.

Using the concurrent engineering approach, suggest the best combination of design and

manufacturing for the gear and pulley system. Assume other necessary data as required. The

component tolerances can be obtained as 3 times the standard deviation of the process.

17. A competitive manufacturing company has to deliver 300 units of a cylindrical part to a

customer. The critical dimension is the diameter of the part, which is to be machined within 1

0.003 in. Suppose there are three alternative machine tools with the information given below in

table

Three manufacturing alternatives are available: engine lathe, automatic screw machine, and NC

lathe. The company wants to know the unit cost of production and manufacturing lead time as

well as the expected no. of defects produced on these machines. This information will be helpful

to the company in considering a trade-off among the unit cost, manufacturing lead time,and

quality represented the number of defects and selecting a machine tool depending on the

customers requirement. Based on this information, advise the selection of machine tools.

The other data are:

Unit raw material cost= $15.00

Unit salvage cost value= $ 1.00

Process average = 1.0005 in.

18. Goldenburg and Associates(GA) have received an order for 500 gears. The primary dimensional

control that GA has to worry about is the pitch circle diameter of the gear, which should be

within 30.002 in. Because this item is being used in a number of products, GA wants to explore

the possibility of using alternative technologies for its manufacture. A preliminary analysis

indicates that a universal milling machine,a Broaching machine with a form type of broaching

cutter, and a hobbing machine are available withn the company. Estimate the unit cost of

production,manufacturing lead time , and expected number of defective gears produced on all

these machine tools. The available data are shown below in table

The other data are:

Unit raw material cost= $10.00

Unit salvage cost value= $2.00

Process average = 3.0002 in.

19. A lot of 1000 units of steel rods 40 cm long and 7 cm in diameter is turned on an NC lathe at a

feed rate of 0.2 mm per revolution and depth of cut 2 mm. The tool life is given by vT0.25=190

The other data are:

Machine labor rate= $10/h

Machine overhead rate = 200 % of labor

Grinding labor rate= $10/h

Grinding overhead rate= 300% of grinding labor

Loading and unloading time= 2 min/piece

Two types of carbide tools can be used for the turning operation: brazed inserts and throwaaway

inserts. The data related to the tools are:

Brazed Inserts

Original cost of the tool= $25.00

Grinding time = 3 min

Tool changing time= 1 min

The tool can be ground only five times before it is discarded.

Throwaway Inserts

Tool cost=$ 15.00

Tool changing time= 0.5 min.

20. A 300 mm diameter part having a 100 mm hole in the center is to be faced starting at the

outside. Determine the machining time if the following data are available:

Spindle rotational speed= 10 revolutions per second

Depth of cut= 4 mm

Feed = 0.10 mm per revolution.

21. A thousand bars 85 mm in diameter and 350 mm in length are to be machined to 84.75 mm in

diameter. Only two cuts are permitted: a rough cut and a finishing cut. The following machining

conditions are used for these cuts:

Rough cut

Cutting speed = 90 m/min

Feed rate= 0.10 mm/rev

Depth of cut=0.1 mm

Finishing cut

Cutting speed = 120 m/min

Feed rate= 0.03

Depth of cut = 0.02 mm

22. Determine the machining time for face milling a workpiece if the cutter width is larger than

workpiece. The following data are given:

Milling cutter has 15 teeth and 60 mm diameter

Rotational speed = 300 rpm

Depth of cut= 4 mm

Feed = 0.020 mm per tooth

Length of workpiece= 400 mm