Question & Answer

What is the difference between fixed routing and variable routing in material transport systems?

Name the five main types of material transport equipment.

What are the principal material handling functions in manufacturing?

What are the main components of an integrated manufacturing system?

The designer of a polar configuration robot is considering a portion of the manipulator consisting of

a rotational joint connected to its output link. The output link is 25 in long and the rotational joint

has a range of 75°. The accuracy of the joint-link combination, expressed as a linear measure at the

end of the link which results from rotating the joint, is specified as 0.030 in. The mechanical

inaccuracies of the joint result in a repeatability error = ±0.030° of rotation. It is assumed that the

link is perfectly rigid, so there are no additional errors due to deflection. (a) Show that the specified

accuracy can be achieved, given the repeatability error. (b) Determine the minimum number of bits

required in the binary register of the robot's control memory to achieve the specified accuracy.

A stepper motor serves as the drive unit for the linear joint of an industrial robot. The joint must

have an accuracy of 0.25 mm. The motor is attached to a leadscrew through a 2:1 gear reduction (2

turns of the motor for 1 turn of the leadscrew). The pitch of the leadscrew is 5.0 mm. The

mechanical errors in the system (due to backlash of the leadscrew and the gear reducer) can be

represented by a normal distribution with standard deviation = ±0.05 mm. Specify the number of

step angles that the motor must have in order to meet the accuracy requirement.

The largest axis of a Cartesian coordinate robot has a total range of 750 mm. It is driven by pulley

system capable of a mechanical accuracy = 0.25 mm and repeatability = ±0.15 mm. Determine the

minimum number of bits required in the binary register for the axis in the robot's control memory.

A DC servomotor drives the y-axis of a NC milling machine table. The motor is coupled to the table

lead screw with a gear reduction of 2:1 (2 turns of the motor shaft for each single rotation of the

lead screw). There are 2 threads per cm in the lead screw. An optical encoder is directly connected

to the lead screw (1:1 gear ratio). The optical encoder emits 100 pulses per revolution. To execute a

certain programmed instruction, the table must move from point (x = 25.0 mm, y = 28.0) to point (x

= 155.0 mm, y = 275.0 mm) in a straight-line trajectory at a feed rate = 200 mm/min. For the y-axis

only, determine: (a) the control resolution of the mechanical system, (b) rotational speed of the

motor, and (c) frequency of the pulse train emitted by the optical encoder at the desired feed rate.

A DC servomotor drives the x-axis of a NC milling machine table. The motor is coupled to the table

lead screw using a 4:1 gear reduction (4 turns of the motor for each turn of the lead screw). The leadscrew pitch = 6.25 mm. An optical encoder is connected to the lead screw. The optical encoder

emits 500 pulses per revolution. To execute a certain programmed instruction, the table must move

from point (x = 87.5 mm, y = 35.0) to point (x = 25.0 mm, y = 180.0 mm) in a straight-line

trajectory at a feed rate = 200 mm/min. Determine (a) the control resolution of the system for the

x-axis only, (b) the corresponding rotational speed of the motor, and (c) frequency of the pulse train

emitted by the optical encoder at the desired feed rate.

An end milling operation is carried out along a straight line path that is 325 mm long. The cut is in a

direction parallel to the x-axis on an NC machining center. Cutting speed = 30 m/min and chip load

= 0.06 mm. The end milling cutter has two teeth and its diameter = 16.0 mm. The x-axis uses a DC

servomotor connected directly to a leadscrew whose pitch = 6.0 mm. The feedback sensing device

is an optical encoder that emits 400 pulses per revolution. Determine (a) feed rate and time to

complete the cut, and (b) rotational speed of the motor and the pulse rate of the encoder at the feed

rate indicated.

A milling operation is performed on an NC machining center. Total travel distance = 300 mm in a

direction parallel to one of the axes of the worktable. Cutting speed = 1.25 m/s and chip load = 0.05

mm. The end milling cutter has four teeth and its diameter = 20.0 mm. The axis uses a DC

servomotor whose output shaft is coupled to a leadscrew with pitch = 6.0 mm. The feedback

sensing device connected to the leadscrew is an optical encoder that emits 250 pulses per

revolution. Determine (a) feed rate and time to complete the cut, and (b) rotational speed of the

motor and the pulse rate of the encoder at the feed rate indicated.

A leadscrew connected directly to a DC servomotor is the drive system for a positioning table. The

leadscrew pitch = 4 mm. The optical encoder attached to the leadscrew emits 250 pulses/rev of the

leadscrew. Determine (a) the control resolution of the system, expressed in linear travel distance of

the table axis, (b) the frequency of the pulse train emitted by the optical encoder when the

servomotor operates at 14 rev/s, and (c) the travel speed of the table at the operating speed of the

motor.

Solve the previous problem only the servomotor is connected to the leadscrew through a gear box

whose reduction ratio = 12:1 (12 revolutions of the motor for each revolution of the leadscrew).

A leadscrew coupled directly to a dc servomotor is used to drive one of the table axes of an NC

milling machine. The leadscrew has 5 threads/in. The optical encoder attached to the leadscrew

emits 100 pulses/rev of the leadscrew. The motor rotates at a maximum speed of 800 rev/min.

Determine (a) the control resolution of the system, expressed in linear travel distance of the table

axis; (b) the frequency of the pulse train emitted by the optical encoder when the servomotor

operates at maximum speed; and (c) the travel speed of the table at the maximum rpm of the motor.

The worktable of a numerical control machine tool is driven by a closed-loop positioning system

which consists of a servomotor, leadscrew, and optical encoder. The leadscrew has 4 threads/in and

is coupled directly to the motor shaft (gear ratio = 1:1). The optical encoder generates 200 pulses

per motor revolution. The table has been programmed to move a distance of 7.5 in at a feed rate =

20.0 in/min. (a) How many pulses are received by the control system to verify that the table has

moved the programmed distance? What are (b) the pulse rate and (c) motor speed that correspond to

the specified feed rate?

An NC machine tool table is powered by a servomotor, leadscrew, and optical encoder. The

leadscrew has a pitch = 5.0 mm and is connected to the motor shaft with a gear ratio of 16:1 (16

turns of the motor for each turn of the leadscrew). The optical encoder is connected directly to the

leadscrew and generates 200 pulses/rev of the leadscrew. The table must move a distance = 100 mm

at a feed rate = 500 mm/min. Determine (a) the pulse count received by the control system to verify

that the table has moved exactly 100 mm; and (b) the pulse rate and (c) motor speed that correspond

to the feed rate of 500 mm/min.

The two axes of an x-y positioning table are each driven by a stepping motor connected to a

leadscrew with a 4:1 gear reduction. The number of step angles on each stepping motor is 200. Each

leadscrew has a pitch = 5.0 mm and provides an axis range = 400.0 mm. There are 16 bits in each

binary register used by the controller to store position data for the two axes. (a) What is the controlresolution of each axis? (b) What are the required rotational speeds and corresponding pulse train

frequencies of each stepping motor in order to drive the table at 600 mm/min in a straight line from

point (25,25) to point (300,150)? Ignore acceleration.

The y-axis of an x-y positioning table is driven by a stepping motor that is connected to a leadscrew

with a 3:1 gear reduction (3 turns of the motor for each turn of the leadscrew). The stepping motor

has 72 step angles. The leadscrew has 5 threads per inch and provides an axis range = 30.0 in. There

are 16 bits in each binary register used by the controller to store position data for the axis. (a) What

is the control resolution of the y-axis? Determine (b) the required rotational speed of the y-axis

stepping motor and (c) the corresponding pulse train frequency to drive the table in a straight line

from point (x = 20 in, y = 25 in) to point (x = 4.5 in, y = 7.5 in) in exactly 30 sec. Ignore

acceleration.

The two axes of an x-y positioning table are each driven by a stepping motor connected to a

leadscrew with a 10:1 gear reduction. The step angle on each stepping motor is 7.5°. Each

leadscrew has a pitch = 5.0 mm and provides an axis range = 300.0 mm. There are 16 bits in each

binary register used by the controller to store position data for the two axes. (a) What is the control

resolution of each axis? (b) What are the required rotational speeds and corresponding pulse train

frequencies of each stepping motor in order to drive the table at 600 mm/min in a straight line from

point (25, 25) to point (100, 150)? Ignore acceleration.

The drive unit of a positioning table for a component insertion machine is based on a stepping

motor and leadscrew mechanism. The specifications are for the table speed to be 25 mm/s over a

600 mm range and for the accuracy to be 0.025 mm. The pitch of the leadscrew = 4.5 mm, and the

gear ratio = 5:1 (5 turns of the motor for each turn of the leadscrew). The mechanical errors in the

motor, gear box, leadscrew, and table connection are characterized by a normal distribution with

standard deviation = 0.005 mm. Determine (a) the minimum number of step angles in the stepping

motor, and (b) the frequency of the pulse train required to drive the table at the desired maximum

speed for the stepping motor in part (a).

The positioning table for a component insertion machine uses a stepping motor and leadscrew

mechanism. The design specifications require a table speed of 40 in/min and an accuracy = 0.0008

in. The pitch of the leadscrew = 0.2 in, and the gear ratio = 2:1 (2 turns of the motor for each turn of

the leadscrew). The mechanical errors in the motor, gear box, leadscrew, and table connection are

characterized by a normal distribution with standard deviation = 0.0001 in. Determine (a) the

minimum number of step angles in the stepping motor, and (b) the frequency of the pulse train

required to drive the table at the desired maximum speed.

The drive unit for a positioning table is driven by a leadscrew directly coupled to the output shaft of

a stepping motor. The pitch of the leadscrew = 0.18 in. The table must have a linear speed = 35

in/min, and a positioning accuracy = 0.001 in. Mechanical errors in the motor, leadscrew, and table

connection are characterized by a normal distribution with standard deviation = 0.0002 in.

Determine (a) the minimum number of step angles in the stepping motor to achieve the accuracy,

(b) the associated step angle, and (c) the frequency of the pulse train required to drive the table at

the desired speed.

A stepping motor with 100 step angles is coupled to a leadscrew through a gear reduction of 9:1 (9

rotations of the motor for each rotation of the leadscrew). The leadscrew has 5 threads/in. The

worktable driven by the leadscrew must move a distance = 10.00 in at a feed rate of 30.0 in/min. Determine (a) number of pulses required to move the table, and (b) the required motor speed and

pulse rate to achieve the desired table speed.

A stepping motor has 200 step angles. Its output shaft is directly coupled to leadscrew with pitch =

0.250 in. A worktable is driven by the leadscrew. The table must move a distance of 5.00 in from its

present position at a travel speed of 20.0 in/min. Determine (a) the number of pulses required to

move the table the specified distance and (b) the required motor speed and pulse rate to achieve the

specified table speed.

Referring to Problem 38.1, the mechanical inaccuracies in the open-loop positioning system can be

described by a normal distribution whose standard deviation = 0.005 mm. The range of the

worktable axis is 500 mm, and there are 12 bits in the binary register used by the digital controller

to store the programmed position. For the positioning system, determine (a) control resolution, (b)

accuracy, and (c) repeatability. (d) What is the minimum number of bits that the binary register

should have so that the mechanical drive system becomes the limiting component on control

resolution?