Experiments in Aligning Threaded Parts Using Hand a Robot

Experiments

in Aligning

Threaded

Using a Robot

Parts

Hand

M. A. Diftler,

March

I. D. Walker*i

5, 1998

Abstract

Techniques angular

position

ing threaded to a bolt nut.

for determining

parts.

These

measuring

Kinematic

models

termined.

The models

the

and

indicate

describe

in-plane

on the direction

relative

currently

the

that

occurs

relationship

and are used to show how to distinguish

a nut connection attitude

of the angular

part

alignment

limited

by using of the

when

how angular

axial bolt

misalignment

during which,

parts

alignment

only.

spinning, in turn,

for align-

"falls"

threaded

the aligned

force data

force and

a nut with respect

the bolt

between

between

using

techniques

are based on backspinning

the force change that

threaded

to augment

new techniques

are introduced

of a bolt

tracking tained

are developed

and

backspinning

cases

data

and correcting

into the during

may be de-

and misaligned In addition, data

by

can be oh-

is used to correct

*M. A. Diftler is with the Automation and Robotics Department, Lockheed Martin, Houston, Texas. E-maih [email protected]. tI. D. Walker is with the Department of Electrical and Computer Engineering, Clemson University, Clemson, South Carolina, 29634 E-mail: [email protected].

the misaligmnent.Resultsfrom experimentsusinga bolt held in a specializedfixture anda threefingeredStanford/JPLhandarepresented. Keywords: ThreadedFasteners,Robot Hands,Bolts, Part Mating, Part Alignment, Force Control.

1

Introduction

Aligning,

and

designer.

Bringing

nut

mating

together

to a low tolerance

intelligence ing,

skills.

or perhaps

properly lator

must

The

the

manipulators

describes with above

all be subdivided, work

between fine

required

steps

Clemson

alignment

the

then

finely

even

start

to bring thread

align

areas

Rice the

University parts

mating,

and

together, prevent 2

machine

mating

and

vision,

proximity.

either

and

artificial

haptic and

sens-

oriented

A manipu-

Either mating

prestored

and

bolt

fixtures.

before

systems

tolerance

be acquired

parts

using

robotics

of robotic

must

the may

same start.

or sensed

tightening

can

in-

only

be

control.

mating

of on-going

a high

or specialized

the

part

position

for successful

more

using

into close

of alignment

and

from

parts

parts

to the

an array

hands,

Actual

of force

University,

needed

to successfully

to bring

are essential

yielding

Both

robot

positions.

a combination

ranging

requires

model.

levels

challenges

be identified

grippers,

both

relative

must

world

must

will perform

that

All of the

device

part,

its cover,

items

alignment

significant

female

and

use of generic

manipulator

accomplished

and

jar

individual

gross

presents

a male

a well structured

perform

formation

parts

plastic

The

through

or another

the

threaded

of threaded

research. the

The

parts, focus

NASA/Johnson

and wedging

the

force

and

and

jamming,

can

of cooperative Space

and

they

position and

Center control recognize

is

task

completion. In a well

constrained

issue.

However

Space

Station

threaded

The

task

fine

alignment [14],

floor,

alignment

environments

position

and

a priori.

may

like on the

orientation

data

Experiments

Testbed

the

determine information

the

initial

using

(DART)

that

previous bolt

that

the

parts

alignment

was part

cross

systems, and

nut

threading

have

for determining following

been

sufficient

backspinning

robotic

more

not

required the

be an

International

to align

Johnson

[6] are addressing

Space

this thread

alignment

is an extension

but even

[11], and and

here

the

[9], [14], have

relied

on the

required

in proper

alignment.

A sufficiently

occurred,

that

the

A torque

successful with

axial

and,

in certain

of previous

force

high

data

and

situations,

research

torque

the relative

not

position

data

to correct

at the Johnson

bolt

just cases,

that

of threads.

to

provide

in most

indicates

set

used

torque

at the

and,

few

achieved.

does

bounds first

force

device

tightening

sensed

information

performed

was

has failed

specific

between

sensing

technique

insertion

within

mating

This

[8], recogniz-

[9] is one of the

force

alignment

fasteners

demonstrating

Fearing

proper

damaged.

along

Nicolson

[16],

when

alignment.

to have

decomposition

[15],[14],[7],

issue,

of threaded

to identify

are

has

manipulation

on task

failures

alignment

necessary

on how to correct

indicates

with

focuses

[5], identifying

resolution

if the

and

deals

[5], [10], [13], [18], [19].

addresses

have

that

issue

implementations that

The

flexible

Robotic

of the literature

In addition,

basis

the

be available

Anthropomorphic

completion

feedback

paper,

more

base,

always

as a factory

issue.

the

did not

such

and

a planetary

will not

majority

avoids

efforts

or on

Dexterous

alignment

ing

in less constrained

parts

Center's

environment,

the

In this

provide

the

alignment. Space

Center

and

presented

relationship

in [3], [4]. between

A specialized data,

threaded

fixture

techniques

Higher part

is used

proper

alignment

are

2

Kinematics

results

indicator

feels the

characteristic

Thread bolt the bolt

threads inserts

and nut

the and

and

nut

used

for the

in a thread the

bolt.

The

cross are

modeled

to the rounded nut

thread,

that

grows

starts from

tooth

of interest

with

pattern.

is aligned as equilateral profiles

that

cross

section

a steel

with

the

turn

with

turning

process. When

the

the

is tapered after

[9]. The

a bolt, This

to

bolt with

(HELICOILrM).

section

cut steel

on the several

order

direction steel

on the tips

test

a person

applications.

start

exist

to full size

part,

a cross

actually bolt

threaded

insert

1 shows

triangles

and

[12].

blindly.

for space

the data.

on the

are a standard

thread

force

in the proper

thread

hardware Figure

the

show

theoretical

hand

the task

parts

at full size, while zero

are doing

axial

misalignments

during

the mating

a helical

section

point

will then

plate

the

to a male

they

in aluminum

follow

correcting

that

and

both

alignment,

type

are used

alignment,

respect

if they

nut

presented

a Stanford/JPL

at some

by people

are

Using

and

with

an aluminum

threads

threads

approximation

used

nut

angular

with

a nut,

the

In this paper,

of this

bolt.

into

models

models.

tested

part,

click of good

and

nut

bolt

is often

the fasteners.

external

and

threaded

of the

alignment

tighten

developed

a female

in a drop

backspinning, the

of 10 to 15 degrees

Backspinning

kinematic

to validate

for identifying

Thread

fidelity

Both cut

nut. off. insert,

bottom

revolutions

the

of both Both

This

the is an

which resulting around

is

Tilt angle: 0L

a(cO hb (P)

ROtates into page

Nut thread

i /_

start

!//

Nut (rotates clockwise)

Front view

Rotates out of page

_ Top view

Figure

2.1

Drop

The

first

bolt

drops

into

parameter

the

will be called

the

starts

part.

nut

"drop

experiments

described

tilt

angles

respect

fit within

with

with the

A 2 point

smaller nut's

bolt

the

azimuth"

contact

and the

nut's

threads. the

problem

cycle.

is defined

the

starts nut

normal. When

bolt defines

the

As the nut

falls into when

plate

the

point

relative

is the

at which

angle, part

from

rotates

while

the

nut

rotates, a cross

point the

its

occurs

the thread

two orientations. bolt

In

is set at various

thread

section

at which

drop

a, between

for each

reaches the

kinematics The

by the

thread

in this work, to the

in backspinning

backspinning

1 shows

diameter,

boundary

of interest

during

Figure

the

contact

2 point

Azimuth

important

of each

1" Bolt-nut

start

of the

bolt

comes that

in will

nut. drop

occurs

and

is used

to calculate

the

local

tilt angle,

or global start.

tilt

Or as a function between

Figure

the

1 illustrates

of a. The

bolt

and

nut

the contact

(a(a)

a(c_) and

start.

These

threads the

The

variables

angle distance actual

BTD/2

or global

the tilt

(a(_)

BTD

the

degrees),

nut

threads

angle,

plane are

component

aligned

of the

with

defined

the

actual

nut

thread

by:

ch)sin(OL)

= ND,

(1)

+ Cx) sin(OL)

= f(p),

(2)

+ ch tan(0t),

2

of c_ since

is half 22.5

between

lies in the

the size of the bolt thread

are a function

(nominally

-

is the

OL,

the constraints

- ch)cos(OL)

define

as it rotates.

taper

vertical

hbt(c_)

tilt angle,

+ (hbt(a)-

cx -

where

that

and

+ cz)cos(0c)

(hbt(c_)

local

the nut

bolt

diameter

ND

is the

in the

plane

0, is calculated

by:

(3)

that

is in contact

with

the

in contact

with

shrinking

comes at the nut

base

diameter,

and

of the and

is a function

bolt

f(p)

nut thread bolt

taper,

is the

of thread

0t is

relevant pitch.

0 = 0L/cos( ).

The

global

tilt angle

may

also be visualized

as the

tilt

(4)

between

the

nut's

angle

on bolt

and

bolt's

vertical

axes. The figure of drop

importance 2. This azimuth,

of equation

figure

shows

ez, in the

the bolt

4 and actual thread

the

drop

azimuth

tilt angle, start,

-rz

alignment

0, at which

a drop

will occur

direction

(figure

1).

The

are seen

in

as a function vertical

line

at

Figure 2: Drop model: tilt vs. drop azimuth (-rz direction) 90 degreesrepresentsa flip from positive to negative tilt anglesand is a discontinuity in the model associatedwith cos90. (This vertical line is a graphical artifact and not part of the predicted tilt angles.) The asymptotesassociatedwith the actual tilt angle, 0, also a result and

of the

270 degrees.

different states

cosine The

directions. that

the

drop This

drop

angles.

tilt

true

for all tilt

directions,

bolt

by tilting

in the

bolt

thread

start. picture

that

global

degrees

which

is nearly

3 shows

of how the

bolt

0, is for the

is approaching

the

to the

the

two

interacts most

point with

part

perpendicular

the

into

result

nut's the

(-90)

and

direction

actual

aligned

for 10 degrees

contact;

the

cross

flats.

same:

yielding

to the

local

from

in simple

two terms

for moderate

threaded

parts

to

and

will be to realign

with

the

of tilt

the

azimuth

c__.

of the

of the

gives

section

a drop tilt

drop

is

in direction

In addition,

page,

-90 degrees

asymptote

misalignment

plane

case

the

same

tilt

well with

to correct

a typical

the

to the

correlates

perpendicular

actually

theoretical

perpendicular

technique

illustrates

are

approaching

important

result

an initial

direction

asymptotes

is actually

theoretical

Figure

tilt,

of the

is an extremely

representation

a clearer the

If this

Two

azimuth

azimuth

high

A CAD

term.

are

plane.

the

bolt

figure

azimuth

shows of-58

Tilt angle = 10.62 degs,

= -58 degs

Azimuth

Nut

start

start

,_

Bolt sta

a: 2 Point contact Figure

2.2

The

Drop

important

For this case the

the

global

tilt

bolt

tilt

angle,

0 [1].

Figure

4 presents

the

defined bolt

can

model,

and

second

the

bolt

fall into two assume the

the

drop that

two point

plane

angle.

by tile global

Next, models

parameter

relevant

up on the

that

2 point

contact

representation

Distance

second

with

3: Typical

b: Bolt crosssection

Prior

relevant

associated of interest

nut

thread

view

thread

is at roughly

angle.

of the

This

backspinning

is the

to a drop

a side

tilt

with

the

global

tilt

minimum

minimum

minimum

tilt

plane.

near

case

from

is the

the

limiting

plane

the

in line

figure

from

the bolt drops.

is the

between

a point

distance

distance

distance This

distance

will fall very

10 degree

is the

nut

next

with

3 and

thread

the

clearly

along

factor

aligned

the

global

shows plane

in how far the

nut. models the

that global

model,

bound tilt

is based

the

angle,

possible 0, does

on a two point

drop not

distance change

contact

that

are after occurs

constructed. the

drop.

after

the

Both The

first

bolt

falls.

Tilt angle = 10.62 degs Azimuth = -58 degs plane

i

Minimum

Nut start

Local model Figure

Within

this

model,

configuration. sufficiently with

respect

the

In the small

point

aligned

tilt

to the

two

4: Side view

angle

nut.

case, such

The

(ad(og)

contact

final

may

figure

that

of typical

position

result

5, the

both

sides after

fall the

= ND

BD

cxd -

+

TO+

dhd-

the

global

the tilt

relevant plane

with

bolt

that

resulting

is obtained

the

+ 2,

- htl(c_g

-

is at a threads

from:

(5)

(6)

DNC)

(7)

tan 30 chd

bolt

in matching

- chd) cosO = dhd

(f(p)

threaded

180) + TCH

(8)

tan 30

parameters

respect

evenly,

shows

or cross

- chd) sinO = NDD

2

In this case

an aligned

section

drop

+ cxd) sinO + (hd(ag)

NDD

case

in either

cross

+ cxd) cosO + (hd(ag)

-(ad(og)

pre-drop

to the

are a function bolt

thread

9

of c_g. _g is an angle start

and

is very

that

similar

quantifies to c_ which

NDD

ND

Figure

identifies

the

direction

5: Two

of the

point

local

tilt

Ah

where

hbt(a)

Figure and

6 shows

the right

of the

drop

is defined

bolt and

in figure

contact

the

final

(adc(ag)

-(adc(ag)

does

drop

plane.

The

= f(hd(ag

- non-cross

actual

-

threading

drop

distance

is calculated

by:

(9)

hbt(a)),

1.

the cross threading thread

.."'

configuration

not fall.

position

after

+ cxdc)

+ cxdc)

Once the

cosO+

that

again, drop

occurs

the tilt angle

is obtained

(hdc(ag)

sin 0 + (hdc(ag)

when

-

chdc)

- chdc)

does

the bolt drops

unevenly

not change

as a result

from:

sin 0 = NDD,

cos 0 = dhdc,

(10)

(11)

BTD cxdc

-

2

+ chdctan(Ot).

10

(12)

dhdc- (f(p) + 2 • DNC)

NDD=ND+

_'_

T-_/

dhdc

_. ............._ adc(ccg)

0Ok%:'

dc,.t

¢c

DNC_I_

Figure

The contact what

drop

is limited happens

extreme in figures constraints nut

second

tooth

model

by the

when

case which 7, 8, and

parallels

the

bolt.

smaller the

drop

in the

in the

than

model

of the

sin(60

d3 + d4

push

nut

of the

threading

slide the

developed

d4

sin 60

This

global

model

is useful

in the

contact

tilt

drop

in [4] for the

pair bolt

of the

bolt

the two point

bolt

displacement

- cross

direction

plane.

contacts

drops drop

to one side The

contact

thread

if;,+

..............

a slide

thread

of plane

predicts

point

assumes

nut

out

are limited and

6: Two

(13)

tan 30

with

two point

relative

to the

tilt

direction.

tilt

contact nut

until

in describing

model,

local

angle

is given

This

is depicted plane.

The

between

one

by:

2 • DNC - O)

--

sin(60

atc(ag)/ sin(120

11

(14)

+ O)

cos 30 - 0)

(15) '

Slide model blow-up:

Figure

7: Slide

hs = DNC,

figure

8

model

2 + d3,

(16)

cos 60,

cs = d3 * sin 60.

where

cs and

hs yield

the

relative

position

of the

two point

contact

(17)

bolt

thread

with

respect

to the

nut

thread. Combining plot

the

a function

nut

slide

discontinuity

threading

plane

data

of displacement

figures the

the

after

change model seen

condition

a drop.

tilt

If out

the

represents in the

then

the

along

angle,

the

two

of plane

bolt's

smaller

drop

discussed

of global

is minimal

for both

model

above. 8.

the

signifies

the

switch

model

two effect

models of thread

will dominate

interaction

12

and figure

than

If the

thread

axis:

drops

The

point

vertical

model

two

bound

the 9.

point

from the

the

is significant,

bolt then

model

yields

As illustrated

In addition

aligned

to the

displacement

a

in the

model.

possible

interaction as the

slide

cross as

outside

of the

global

comes

to rest

in the

displacement

will

the

i

/

_

...................

:i

/:

d3

,' ..........

i

30

/"

'i/"

.................. :......... \ oo __

(60 ±0)

Figure

8: Slide

model

(60+0)

blow-up

o_

Z TWO poinl n_del Glide rrtldel

-[

]

oo_

OO4

oea

oo2

-