Ci a ion: Pas o , R.; Mihola, M.;
Zeman, Z.; Bolesla ský, A.
Knowledge-Based Au oma ed
Mechanical Design o a Robo
Manipula o . Appl. Sci. 2022,12, 5897.
h ps://doi.o g/10.3390/
app12125897
Academic Edi o s: Ahmad Ba a i and
Ma cos de Sales Gue a Tsuzuki
Recei ed: 8 Ap il 2022
Accep ed: 7 June 2022
Published: 9 June 2022
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applied
sciences
A icle
Knowledge-Based Au oma ed Mechanical Design o a
Robo Manipula o
Robe Pas o * , Milan Mihola , Zdenˇek Zeman and Adam Bolesla ský
Depa men o Robo ics, Facul y o Mechanical Enginee ing, VSB-TU Os a a, 70800 Os a a, Czech Republic;
[email p o ec ed] (M.M.); [email p o ec ed] (Z.Z.); [email p o ec ed] (A.B.)
*Co espondence: [email p o ec ed]; Tel.: +420-737-570-794
Abs ac :
Design me hods ha e been imp o ing wi h an inc easing le el o algo i hmic suppo o
some ime. The mos ecen ad ances include gene a i e design and a ious op imiza ion me hods.
Howe e , he au oma ed design ools a e o en ocused on a single s age o he design p ocess, o
example, kinema ics design, mechanical opology, o d i e selec ion. In his pape , we show he
whole design p ocess o a obo ic manipula o in an au oma ed wo k low. The me hod consis ed o
wo main pa s: a gene ic op imiza ion o he kinema ic s uc u e and an i e a i e au oma ed CAD
design. The me hod was hen applied o a case s udy in which a manipula o wi h i e deg ees o
eedom o a handling ask was designed.
Keywo ds:
kinema ics op imiza ion; modula manipula o ; gene ic op imiza ion; knowledge-based
sys em; au oma ed CAD design
1. In oduc ion
When obo s in manu ac u ing a e conce ned, we o en hink o hei uni e sali y
as a good hing. Howe e , a case can be made o he u ili y o a obo which is ailo ed
o a speci ic ask, in he sense o a single-pu pose machine. Such a obo would ha e
he kinema ic s uc u e op imized o he ask a hand and hypo he ically should be mo e
ene gy e icien han a uni e sal obo , which mus ca y i s d i e uni s e en i he ask
does no equi e hei use.
This single-pu pose obo would need o be designed on a ask-speci ic basis. Ne -
e heless, op imizing he kinema ics, designing, manu ac u ing, and assembling a whole
new obo is a leng hy p ocess ha equi es a lo o expe ise and ime. The p ocess o
c ea ing a new obo o a speci ic ask would equi e conside able esou ces, and he
p o i abili y o such a sys em is unce ain, e en i i p omises lowe ope a ing cos s. The
e u n o in es men becomes in e es ing when we s a lowe ing he cos o designing
he ask-speci ic obo . To educe he cos o he design p ocess cos , we need a obus
me hodology wi h as much au oma ion as possible. Ideally, ins ead o ha ing a eam o
expe enginee s designing he obo , we would ha e a compu e p og am ha one pe son
could use o explo e he design possibili ies.
Pa ame ic CAD so wa e packages can alle ia e many o he ou ine design p ocesses
in gene al enginee ing asks, e.g., bol placemen . Fo mo e domain-speci ic design asks,
he e is a me hod usually e e ed o as Knowledge-Based Enginee ing (KBE). The e a e
many de ini ions o KBE sys ems [
1
]. An elabo a e desc ip ion is gi en by Chapman and
Pin old [
2
] in which hey s a e ha ‘KBE ep esen s an e olu iona y s ep in Compu e -
Aided Enginee ing (CAE) and is an enginee ing me hod ha ep esen s a me ging o Objec -
O ien ed P og amming (OOP), a i icial in elligence (AI) and Compu e -Aided Design
(CAD) echnologies, gi ing bene i o cus omized o a ian design au oma ion solu ions.
Many KBE me hods a e buil on a se o design ules o a decision ee [
3
]. Howe e ,
some sys ems do inco po a e op imiza ions o he design. Xu e al. [
4
] ha e implemen ed a
Appl. Sci. 2022,12, 5897. h ps://doi.o g/10.3390/app12125897 h ps://www.mdpi.com/jou nal/applsci
Appl. Sci. 2022,12, 5897 2 o 14
mul i-objec i e pa e o op imiza ion algo i hm o deal wi h di e se design objec i es and
cons ains. A knowledge-based sys em o con aine ship ca go ank s uc u al design was
p esen ed by Cui and Wang [
5
]. Thei app oach employs Mul i-island Gene ic Algo i hms
as a las s ep in he design p ocess. La Rocca e al. [
6
] used s uc u al analysis and mul i-le el
op imiza ion o ai c a wings in hei gene a i e model o ai c a wings. Op imiza ions
in KBE can ake many o ms, whe he i is an op imiza ion o mechanism opology and
s uc u e [
5
,
7
] o a opological op imiza ion o indi idual pa s o mul iple pa s a once [
8
].
In Figu e 1, a gene ic s uc u e o a KBE sys em is indica ed, simila s uc u es can be
ound in [
1
,
9
–
11
]. An in e es ing ea u e o op imiza ions in KBE sys ems is he placemen
o he op imiza ion s ep. Some esea che s ha e placed he op imiza ion unc ion block
owa ds he beginning o he design p ocess. Some conside op imiza ion o be one o he
las s eps in he p ocess [
5
]. This di e ence is mos likely due o he design ules ha a e
being applied in he p ocess and he na u e o he op imiza ion.
Appl. Sci. 2022, 12, 5897 2 o 13
Many KBE me hods a e buil on a se o design ules o a decision ee [3]. Howe e ,
some sys ems do inco po a e op imiza ions o he design. Xu e al. [4] ha e implemen ed
a mul i-objec i e pa e o op imiza ion algo i hm o deal wi h di e se design objec i es and
cons ains. A knowledge-based sys em o con aine ship ca go ank s uc u al design was
p esen ed by Cui and Wang [5]. Thei app oach employs Mul i-island Gene ic Algo i hms
as a las s ep in he design p ocess. La Rocca e al. [6] used s uc u al analysis and mul i-
le el op imiza ion o ai c a wings in hei gene a i e model o ai c a wings. Op imi-
za ions in KBE can ake many o ms, whe he i is an op imiza ion o mechanism opology
and s uc u e [5,7] o a opological op imiza ion o indi idual pa s o mul iple pa s a
once [8].
In Figu e 1, a gene ic s uc u e o a KBE sys em is indica ed, simila s uc u es can be
ound in [1,9–11]. An in e es ing ea u e o op imiza ions in KBE sys ems is he placemen
o he op imiza ion s ep. Some esea che s ha e placed he op imiza ion unc ion block
owa ds he beginning o he design p ocess. Some conside op imiza ion o be one o he
las s eps in he p ocess [5]. This di e ence is mos likely due o he design ules ha a e
being applied in he p ocess and he na u e o he op imiza ion.
Figu e 1. Gene ic s uc u e o a Knowledge-Based Enginee ing Sys em.
Kinema ic s uc u es o obo s a e o en a subjec o op imiza ions in he ield o e o-
lu iona y obo ics [12–14]. In his pape we ook a simila e olu iona y app oach o he
design o kinema ic s uc u e o manipula o s.
Al hough KBE me hods a e used ac oss enginee ing ields, he au ho s ha e no
ound a simila app oach o p oduce a iable mechanical design o ask-based obo s in
he li e a u e. I should be s a ed ha in mos case s udies in he li e a u e, a KBE sys em
is buil on op o he al eady unc ioning design p ocess in o de o make i as e and
mo e e icien . In his s udy, he au ho s aimed o p esen a KBE me hod o design single-
pu pose manipula o s o eplace uni e sal obo manipula o s o simple asks.
This pape is s uc u ed as ollows; Sec ion 2 in oduces he me hod o e iew, Sec-
ion 2.1 desc ibes gene ic op imiza ions o a kinema ic s uc u e, Sec ion 2.2 discusses a
CAD model design and i e a i e design o indi idual mechanism links, and Sec ion 3 hen
uses hese me hods in a case s udy.
2. Ma e ials and Me hods
The me hod o e iew is shown in Figu e 2. Fi s , he basic equi emen s and inpu
pa ame e s needed o s a he obo ic a m design we e de ined, such as he weigh and
dimensions o he manipula ed objec , a ge posi ions o he ajec o y, he equi ed
mo emen ime, and he dimensions o he wo kspace wi h obs acles. In S ep 2, we es i-
ma ed he size o he end e ec o based on he manipula ed objec dimensions. This s ep
was in en ionally chosen o be e y gene ic. Since we did no ye know he o ces ac ing
on he end-e ec o o design o selec he app op ia e end-e ec o , we ook only he size
in o conside a ion and es ima e he olume en elope o he end-e ec o . The size o he
end-e ec o olume was es ima ed o be 1.5 imes he maximum dimensions o he ma-
nipula ed objec .
Figu e 1. Gene ic s uc u e o a Knowledge-Based Enginee ing Sys em.
Kinema ic s uc u es o obo s a e o en a subjec o op imiza ions in he ield o
e olu iona y obo ics [
12
–
14
]. In his pape we ook a simila e olu iona y app oach o he
design o kinema ic s uc u e o manipula o s.
Al hough KBE me hods a e used ac oss enginee ing ields, he au ho s ha e no ound
a simila app oach o p oduce a iable mechanical design o ask-based obo s in he
li e a u e. I should be s a ed ha in mos case s udies in he li e a u e, a KBE sys em is
buil on op o he al eady unc ioning design p ocess in o de o make i as e and mo e
e icien . In his s udy, he au ho s aimed o p esen a KBE me hod o design single-pu pose
manipula o s o eplace uni e sal obo manipula o s o simple asks.
This pape is s uc u ed as ollows; Sec ion 2in oduces he me hod o e iew,
Sec ion 2.1 desc ibes gene ic op imiza ions o a kinema ic s uc u e, Sec ion 2.2 discusses a
CAD model design and i e a i e design o indi idual mechanism links, and Sec ion 3 hen
uses hese me hods in a case s udy.
2. Ma e ials and Me hods
The me hod o e iew is shown in Figu e 2. Fi s , he basic equi emen s and inpu
pa ame e s needed o s a he obo ic a m design we e de ined, such as he weigh and
dimensions o he manipula ed objec , a ge posi ions o he ajec o y, he equi ed
mo emen ime, and he dimensions o he wo kspace wi h obs acles. In S ep 2, we
es ima ed he size o he end e ec o based on he manipula ed objec dimensions. This
s ep was in en ionally chosen o be e y gene ic. Since we did no ye know he o ces
ac ing on he end-e ec o o design o selec he app op ia e end-e ec o , we ook only he
size in o conside a ion and es ima e he olume en elope o he end-e ec o . The size o
he end-e ec o olume was es ima ed o be 1.5 imes he maximum dimensions o he
manipula ed objec .
Appl. Sci. 2022,12, 5897 3 o 14
Appl. Sci. 2022, 12, 5897 3 o 13
Figu e 2. Ou KBE sys em s uc u e o designing obo manipula o s.
S ep 3 o he p ocess was a gene ic op imiza ion o he kinema ic chain. The dimen-
sions o he manipula ed objec s, he end-e ec o , and he obs acles we e used o collision
checking du ing his s ep. The ou pu o his block was a kinema ic chain desc ibed as
ans o ma ion be ween join s and he posi ions, eloci ies, and accele a ions in join
space. Sec ion 2.1 desc ibes his s ep in mo e de ail.
In S ep 4 he end-e ec o was chosen, based on he manipula ed objec pa ame e s,
i.e., dimensions, weigh , and accele a ions du ing manipula ion. The selec ion o he end-
e ec o ollowed he manu ac u e ’s ins uc ions. The las manipula o link was designed
o be compa ible wi h he selec ed end-e ec o . A p elimina y 3D model o he manipu-
la o was designed o i he op imized kinema ic s uc u e. A da abase o a ailable d i e
uni s was p epa ed in ad ance. Howe e , he p elimina y design was assembled om
only he smalles a ailable d i e uni s in he da abase. The s uc u al componen s we e
also minimized by selec ing he smalles a ailable c oss sec ion. This p elimina y 3D
model was analyzed o possible collisions. I a collision is de ec ed in his s ep, i is nec-
essa y o change he kinema ic s uc u e o he manipula o . I no collisions a e de ec ed,
he design can con inue o S ep 5.
In his s ep, he indi idual links o he manipula o we e i e a i ely modeled. The
i e a ions included he selec ion o d i e uni s, kinema ic and dynamic analyses, shape
op imiza ions, and o he necessa y s eps. In he case ha all he indi idual pa s a e de-
signed success ully, he esul is a ull 3D model o he manipula o . I a any poin he
design i e a ion ails, i is necessa y o modi y he kinema ic s uc u e. The pa ame e s o
op imizing he kinema ic s uc u e a e upda ed, and a new op imiza ion is ca ied ou .
Figu e 2. Ou KBE sys em s uc u e o designing obo manipula o s.
S ep 3 o he p ocess was a gene ic op imiza ion o he kinema ic chain. The dimensions
o he manipula ed objec s, he end-e ec o , and he obs acles we e used o collision
checking du ing his s ep. The ou pu o his block was a kinema ic chain desc ibed as
ans o ma ion be ween join s and he posi ions, eloci ies, and accele a ions in join space.
Sec ion 2.1 desc ibes his s ep in mo e de ail.
In S ep 4 he end-e ec o was chosen, based on he manipula ed objec pa ame e s,
i.e., dimensions, weigh , and accele a ions du ing manipula ion. The selec ion o he end-
e ec o ollowed he manu ac u e ’s ins uc ions. The las manipula o link was designed
o be compa ible wi h he selec ed end-e ec o . A p elimina y 3D model o he manipula o
was designed o i he op imized kinema ic s uc u e. A da abase o a ailable d i e uni s
was p epa ed in ad ance. Howe e , he p elimina y design was assembled om only
he smalles a ailable d i e uni s in he da abase. The s uc u al componen s we e also
minimized by selec ing he smalles a ailable c oss sec ion. This p elimina y 3D model
was analyzed o possible collisions. I a collision is de ec ed in his s ep, i is necessa y o
change he kinema ic s uc u e o he manipula o . I no collisions a e de ec ed, he design
can con inue o S ep 5.
Appl. Sci. 2022,12, 5897 4 o 14
In his s ep, he indi idual links o he manipula o we e i e a i ely modeled. The
i e a ions included he selec ion o d i e uni s, kinema ic and dynamic analyses, shape
op imiza ions, and o he necessa y s eps. In he case ha all he indi idual pa s a e
designed success ully, he esul is a ull 3D model o he manipula o . I a any poin he
design i e a ion ails, i is necessa y o modi y he kinema ic s uc u e. The pa ame e s o
op imizing he kinema ic s uc u e a e upda ed, and a new op imiza ion is ca ied ou .
2.1. Kinema ic Syn hesis h ough Op imiza ion
The op imiza ion ook place as he second unc ion block in ou KBE sys em. I
op imizes a kinema ic s uc u e o a manipula o o he unc ionali ies speci ied in he i s
block. The op imiza ion is based on a gene ic algo i hm implemen a ion om MATLAB
Global Op imiza ion Toolbox. The algo i hm c ea es a andom popula ion o indi iduals,
e alua es hei i ness, and c ea es a new popula ion om he indi iduals wi h he bes
i ness alue. In his case, he indi iduals a e desc ip ions o obo kinema ics. The
e alua ion and calcula ion o he i ness unc ion was implemen ed on op o he MATLAB
Robo ics Sys ems Toolbox.
2.1.1. Robo Geno ype Encoding
The obo kinema ic s uc u es a e in he GA op imiza ion ep esen ed by a geno ype
ec o . The s uc u e o a geno ype ec o o a 3 deg ee-o - eedom (DOF) manipula o is
shown in Table 1. The geno ype is a combina ion o link leng hs and join ype. The leng h
o he geno ype depends on he numbe o DOFs in he obo and is se be o e op imiza ion.
Table 1. Robo Geno ype S uc u e.
Pa ame e a1α1a2α2a3α3
Desc ip ion Link 1 leng h Join 1 ype Link 2 leng h Join 2 ype Link 3 leng h Join 3 ype
Uppe bound 1000 2 1000 2 1000 2
Lowe bound 275 0 250 0 225 0
The geno ype ec o is a ec o o in ege s. The leng h is gi en in millime e s. The
lowe bound o he link leng h is di e en o each link. This is because we expec ed he
join s owa ds he base o ha e mo e powe ul and he e o e bigge d i e uni s. Towa ds
he end e ec o , he equi emen s o join o que a e gene ally lowe han in he base, and
we could expec smalle d i e uni s. The bounds can be modi ied o di e en applica-
ions. Wi h ou selec ed d i e uni s, we ha e se led on lowe bounds d i en by a linea
unc ion (1)
. The maximum leng h is less impo an , since he i ness unc ion is ying o
minimize he leng h o he whole manipula o . Fo ou expe imen s we ha e used 1000
which was mo e han enough o he used wo kspaces.
an=300 −n·25 [mm](1)
whe e: nis he link numbe and an is he leng h o he n h link.
The join ype desc ibes he o a ion o a join ela i e o he p e ious join , o in he
case o he i s join ela i e o he wo ld coo dina e ame. We ha e used h ee di e en
o ien a ions shown in Figu e 3. The ans o ma ion ma ices o hese join ypes a e de ined
in Equa ion (2).
Appl. Sci. 2022,12, 5897 5 o 14
αi=0→Ti=




cos(θi)
−sin(θi)
0
0
sin(θi)
cos(θi)
0
0
0
0
1
0
ai
0
0
1




αi=1→Ti=




cos(θi)
−sin(θi)
0
0
0
0
−1
0
sin(θi)
cos(θi)
0
0
ai
0
0
1




αi=2→Ti=




0
−sin (θi)
cos(θi)
0
0
cos(θi)
sin(θi)
0
−1
0
0
0
ai
0
0
1




(2)
Appl. Sci. 2022, 12, 5897 4 o 13
2.1. Kinema ic Syn hesis h ough Op imiza ion
The op imiza ion ook place as he second unc ion block in ou KBE sys em. I op i-
mizes a kinema ic s uc u e o a manipula o o he unc ionali ies speci ied in he i s
block. The op imiza ion is based on a gene ic algo i hm implemen a ion om MATLAB
Global Op imiza ion Toolbox. The algo i hm c ea es a andom popula ion o indi iduals,
e alua es hei i ness, and c ea es a new popula ion om he indi iduals wi h he bes
i ness alue. In his case, he indi iduals a e desc ip ions o obo kinema ics. The e alu-
a ion and calcula ion o he i ness unc ion was implemen ed on op o he MATLAB Ro-
bo ics Sys ems Toolbox.
2.1.1. Robo Geno ype Encoding
The obo kinema ic s uc u es a e in he GA op imiza ion ep esen ed by a geno ype
ec o . The s uc u e o a geno ype ec o o a 3 deg ee-o - eedom (DOF) manipula o
is shown in Table 1. The geno ype is a combina ion o link leng hs and join ype. The
leng h o he geno ype depends on he numbe o DOFs in he obo and is se be o e
op imiza ion.
Table 1. Robo Geno ype S uc u e.
Pa ame e a
1
α
1
a
2
α
2
a
3
α
3
Desc ip ion Link 1
leng h
Join 1
ype
Link 2
leng h
Join 2
ype
Link 3
leng h
Join 3
ype
Uppe bound 1000 2 1000 2 1000 2
Lowe bound 275 0 250 0 225 0
The geno ype ec o is a ec o o in ege s. The leng h is gi en in millime e s. The
lowe bound o he link leng h is di e en o each link. This is because we expec ed he
join s owa ds he base o ha e mo e powe ul and he e o e bigge d i e uni s. Towa ds
he end e ec o , he equi emen s o join o que a e gene ally lowe han in he base,
and we could expec smalle d i e uni s. The bounds can be modi ied o di e en appli-
ca ions. Wi h ou selec ed d i e uni s, we ha e se led on lowe bounds d i en by a linea
unc ion (1). The maximum leng h is less impo an , since he i ness unc ion is ying o
minimize he leng h o he whole manipula o . Fo ou expe imen s we ha e used 1000
which was mo e han enough o he used wo kspaces.
𝑎=300 − 𝑛⋅25 󰇟mm󰇠 (1)
whe e: n is he link numbe and an is he leng h o he n h link.
The join ype desc ibes he o a ion o a join ela i e o he p e ious join , o in he
case o he i s join ela i e o he wo ld coo dina e ame. We ha e used h ee di e en
o ien a ions shown in Figu e 3. The ans o ma ion ma ices o hese join ypes a e de-
ined in Equa ion (2).
Figu e 3. Join ypes; (a) α = 0, (b) α = 1, (c) α = 2.
Figu e 3. Join ypes; (a)α= 0, (b)α= 1, (c)α= 2.
T ans o ma ion ma ices o an example 3 DOF kinema ic s uc u e wi h he geno ype
[300, 0, 400, 0, 200, 1] a e shown in (3).
TE=




cos(θ1)
−sin(θ1)
0
0
sin(θ1)
cos(θ1)
0
0
0
0
1
0
0.3
0
0
1




·




cos(θ2)
−sin(θ2)
0
0
sin(θ2)
cos(θ2)
0
0
0
0
1
0
0.4
0
0
1




·




cos(θ3)
−sin(θ3)
0
0
0
0
−1
0
sin(θ3)
cos(θ3)
0
0
0.2
0
0
1



(3)
whe e T
E
is he ans o ma ion ma ix om he base coo dina e ame o he end e ec o
coo dina e ame and [θ1,θ2,θ3] is he cu en join con igu a ion.
2.1.2. E alua ion
The gene ic algo i hm (GA) wo ks by e alua ing each po en ially op imal manipula o
kinema ics using a cos unc ion. This cos unc ion is a weigh ed sum o h ee
alues (3)
:
he posi ioning e o o he manipula o (4), i s leng h (5), and a measu e o collisions
(Figu e 4). The weigh s we e expe imen ally se as weigh 1= 100, weigh 2= 1, weigh 3= 10.
cos =weigh1·cos 1+weigh2·cos 2+weigh3·cos 3(4)
Appl. Sci. 2022, 12, 5897 6 o 13
Figu e 4. Collision measu e calcula ion.
2.2. Cad Model
In p e ious s eps, he dimensions o he end-e ec o we e es ima ed. The i s s ep
in designing a obo ic a m is he selec ion o a eal usable end-e ec o . End-e ec o s o
manipula ion asks we e selec ed based on he shape and dimensions o he handled ob-
jec , on he posi ion o he g ipping su aces, on he accele a ions and ex e nal o ces, and
on he way ha he handled objec is placed in he en i onmen . In his s udy, we consid-
e ed only a ailable o - he-shel end-e ec o s. Thei selec ion ollowed he ins uc ion o
he manu ac u e , using he so wa e ools a ailable on he manu ac u e s’ websi es [15–
17].
Based on he end-e ec o connec ion lange and he p oposed kinema ic s uc u e, a
p elimina y CAD model o he whole a m was c ea ed. The model was assembled using
he smalles d i e uni s a ailable in he da abase and we e used in all he join s. The di-
mensions o he s uc u al elemen s o he obo ic a m hen depend on he d i e uni s
connec ing dimensions. This manipula o model wi h he smalles d i e uni s was hen
subjec ed o analysis, wi h he aim o inding possible collisions be ween he indi idual
pa s o he manipula o i sel and wi hin he en i e wo kplace. I collisions a e ound, he
p oposed kinema ic s uc u e is no accep ed, and he design p ocess e u ns o he kine-
ma ic op imiza ion s ep. Howe e , he inpu pa ame e s o he op imiza ion we e ad-
jus ed in such a way as o e lec he easons why i was no possible o p oceed o he nex
design s age. Fo example, he lowe and uppe bounds o he link leng hs we e adjus ed.
I no collisions a e ound, he p ocess con inues o he nex s ep in which he indi idual
pa s o he obo ic a m a e designed.
2.2.1. n- h Link Design
In his s ep, he o ce and o que e ec s we e aken in o accoun . The indi idual ele-
men s o he manipula o we e designed i e a i ely, beginning om he end-e ec o o-
wa ds he base. Thus, he i s p oposed elemen is he pa connec ing he end e ec o
wi h he nex d i e uni . Figu es 5 and 6 a e low cha s ha desc ibe he design and gen-
e al p ocedu e o he n- h componen , including he espec i e d i e uni s. The design
p ocess depends on he link leng h. Sho links consis o one s uc u al elemen and long
links om h ee elemen s.
Figu e 5. Design p ocedu e o he n- h link i he link consis s o one elemen .
Figu e 4. Collision measu e calcula ion.

Appl. Sci. 2022,12, 5897 6 o 14
The e alua ion was pe o med using he Robo ic Sys em Toolbox in MATLAB. Fo each
indi idual in a GA gene a ion, a igidBodyT ee objec was c ea ed based on he encoded
genes. This objec ep esen s he obo and is used o calcula e he in e se kinema ics (IK)
and collisions. A join con igu a ion was calcula ed using IK o all a ge poin s. The
magni ude o he pose e o was e u ned by he IK solu ion as PoseE o No m. The alue
o cos 1 is he a e age o PoseE o No m alues o all ajec o y poin s.
cos 1=1
n
n
∑
i=1
PoseE o No mi(5)
Thesecondpa o he cos unc ionis asimple sumo heleng hs o he
manipula o segmen s
.
cos 2=
n
∑
i=1
ai(6)
The hi d pa o he cos unc ion is a measu e o collisions. This alue uses he
chceckCollision unc ion o measu e collisions be ween he manipula o and he wo kspace
obs acles. This collision check was done o all a ge con igu a ions.
2.2. Cad Model
In p e ious s eps, he dimensions o he end-e ec o we e es ima ed. The i s s ep
in designing a obo ic a m is he selec ion o a eal usable end-e ec o . End-e ec o s o
manipula ion asks we e selec ed based on he shape and dimensions o he handled objec ,
on he posi ion o he g ipping su aces, on he accele a ions and ex e nal o ces, and on
he way ha he handled objec is placed in he en i onmen . In his s udy, we conside ed
only a ailable o - he-shel end-e ec o s. Thei selec ion ollowed he ins uc ion o he
manu ac u e , using he so wa e ools a ailable on he manu ac u e s’ websi es [15–17].
Based on he end-e ec o connec ion lange and he p oposed kinema ic s uc u e, a
p elimina y CAD model o he whole a m was c ea ed. The model was assembled using
he smalles d i e uni s a ailable in he da abase and we e used in all he join s. The
dimensions o he s uc u al elemen s o he obo ic a m hen depend on he d i e uni s
connec ing dimensions. This manipula o model wi h he smalles d i e uni s was hen
subjec ed o analysis, wi h he aim o inding possible collisions be ween he indi idual
pa s o he manipula o i sel and wi hin he en i e wo kplace. I collisions a e ound,
he p oposed kinema ic s uc u e is no accep ed, and he design p ocess e u ns o he
kinema ic op imiza ion s ep. Howe e , he inpu pa ame e s o he op imiza ion we e
adjus ed in such a way as o e lec he easons why i was no possible o p oceed o he
nex design s age. Fo example, he lowe and uppe bounds o he link leng hs we e
adjus ed. I no collisions a e ound, he p ocess con inues o he nex s ep in which he
indi idual pa s o he obo ic a m a e designed.
2.2.1. n- h Link Design
In his s ep, he o ce and o que e ec s we e aken in o accoun . The indi idual
elemen s o he manipula o we e designed i e a i ely, beginning om he end-e ec o
owa ds he base. Thus, he i s p oposed elemen is he pa connec ing he end e ec o
wi h he nex d i e uni . Figu es 5and 6a e low cha s ha desc ibe he design and gene al
p ocedu e o he n- h componen , including he espec i e d i e uni s. The design p ocess
depends on he link leng h. Sho links consis o one s uc u al elemen and long links
om h ee elemen s.
Appl. Sci. 2022,12, 5897 7 o 14
Appl. Sci. 2022, 12, 5897 6 o 13
Figu e 4. Collision measu e calcula ion.
2.2. Cad Model
In p e ious s eps, he dimensions o he end-e ec o we e es ima ed. The i s s ep
in designing a obo ic a m is he selec ion o a eal usable end-e ec o . End-e ec o s o
manipula ion asks we e selec ed based on he shape and dimensions o he handled ob-
jec , on he posi ion o he g ipping su aces, on he accele a ions and ex e nal o ces, and
on he way ha he handled objec is placed in he en i onmen . In his s udy, we consid-
e ed only a ailable o - he-shel end-e ec o s. Thei selec ion ollowed he ins uc ion o
he manu ac u e , using he so wa e ools a ailable on he manu ac u e s’ websi es [15–
17].
Based on he end-e ec o connec ion lange and he p oposed kinema ic s uc u e, a
p elimina y CAD model o he whole a m was c ea ed. The model was assembled using
he smalles d i e uni s a ailable in he da abase and we e used in all he join s. The di-
mensions o he s uc u al elemen s o he obo ic a m hen depend on he d i e uni s
connec ing dimensions. This manipula o model wi h he smalles d i e uni s was hen
subjec ed o analysis, wi h he aim o inding possible collisions be ween he indi idual
pa s o he manipula o i sel and wi hin he en i e wo kplace. I collisions a e ound, he
p oposed kinema ic s uc u e is no accep ed, and he design p ocess e u ns o he kine-
ma ic op imiza ion s ep. Howe e , he inpu pa ame e s o he op imiza ion we e ad-
jus ed in such a way as o e lec he easons why i was no possible o p oceed o he nex
design s age. Fo example, he lowe and uppe bounds o he link leng hs we e adjus ed.
I no collisions a e ound, he p ocess con inues o he nex s ep in which he indi idual
pa s o he obo ic a m a e designed.
2.2.1. n- h Link Design
In his s ep, he o ce and o que e ec s we e aken in o accoun . The indi idual ele-
men s o he manipula o we e designed i e a i ely, beginning om he end-e ec o o-
wa ds he base. Thus, he i s p oposed elemen is he pa connec ing he end e ec o
wi h he nex d i e uni . Figu es 5 and 6 a e low cha s ha desc ibe he design and gen-
e al p ocedu e o he n- h componen , including he espec i e d i e uni s. The design
p ocess depends on he link leng h. Sho links consis o one s uc u al elemen and long
links om h ee elemen s.
Figu e 5. Design p ocedu e o he n- h link i he link consis s o one elemen .
Figu e 5. Design p ocedu e o he n- h link i he link consis s o one elemen .
Appl. Sci. 2022, 12, 5897 7 o 13
Figu e 6. Design p ocedu e o he n- h link i he link consis s o h ee elemen s.
As pa o his p ocedu e, we di ided he elemen s o he obo ic a m in o wo main
ca ego ies. The i s con ains o - he-shel o o he wise eused o e elemen s (d i e uni s,
end e ec o s, senso s, e c.), o which we canno change he pa ame e s, shape, o indi-
idual dimensions. The second ca ego y con ains mainly load-bea ing and connec ing el-
emen s, which we e designed on he basis o p ede ined ules, bu we can change he
shape, dimensions, and selec ed pa ame e s (e.g., ma e ial). Based on he leng hs o he
indi idual links in he p oposed kinema ic s uc u e o he obo ic a m, one o he wo
design pa hs o he n h elemen was chosen.
The leng h o he kinema ic n-link was compa ed o he diame e o he p e ious (n
− 1) link’s d i e uni , o in he case o he i s link, he end-e ec o leng h was used. I he
leng h o he n-link exceeds he size o he d i e uni (o end-e ec o ) size by mo e han a
ac o o ou , we conside ed i long enough o be buil om h ee elemen s bol ed,
welded, o glued oge he . O he wise, he n- h link will be buil om jus one s uc u al
elemen . Figu e 7 shows examples o links designed om one and h ee s uc u al ele-
men s.
Figu e 7. Examples o he n- h link; (a) om one pa , (b) om h ee pa s.
I he link consis s o one piece o ma e ial, kinema ic and dynamic analysis o he
manipula o ’s 3D model is pe o med i s . Wi hin hese analyzes, a 3D model c ea ed on
Figu e 6. Design p ocedu e o he n- h link i he link consis s o h ee elemen s.
As pa o his p ocedu e, we di ided he elemen s o he obo ic a m in o wo main
ca ego ies. The i s con ains o - he-shel o o he wise eused o e elemen s (d i e uni s,
end e ec o s, senso s, e c.), o which we canno change he pa ame e s, shape, o indi-
idual dimensions. The second ca ego y con ains mainly load-bea ing and connec ing
elemen s, which we e designed on he basis o p ede ined ules, bu we can change he
shape, dimensions, and selec ed pa ame e s (e.g., ma e ial). Based on he leng hs o he
indi idual links in he p oposed kinema ic s uc u e o he obo ic a m, one o he wo
design pa hs o he n h elemen was chosen.
The leng h o he kinema ic n-link was compa ed o he diame e o he p e ious
(n
−
1) link’s d i e uni , o in he case o he i s link, he end-e ec o leng h was used.
I he leng h o he n-link exceeds he size o he d i e uni (o end-e ec o ) size by mo e
han a ac o o ou , we conside ed i long enough o be buil om h ee elemen s bol ed,
welded, o glued oge he . O he wise, he n- h link will be buil om jus one s uc u al
elemen . Figu e 7shows examples o links designed om one and h ee s uc u al elemen s.
Appl. Sci. 2022,12, 5897 8 o 14
Appl. Sci. 2022, 12, 5897 7 o 13
Figu e 6. Design p ocedu e o he n- h link i he link consis s o h ee elemen s.
As pa o his p ocedu e, we di ided he elemen s o he obo ic a m in o wo main
ca ego ies. The i s con ains o - he-shel o o he wise eused o e elemen s (d i e uni s,
end e ec o s, senso s, e c.), o which we canno change he pa ame e s, shape, o indi-
idual dimensions. The second ca ego y con ains mainly load-bea ing and connec ing el-
emen s, which we e designed on he basis o p ede ined ules, bu we can change he
shape, dimensions, and selec ed pa ame e s (e.g., ma e ial). Based on he leng hs o he
indi idual links in he p oposed kinema ic s uc u e o he obo ic a m, one o he wo
design pa hs o he n h elemen was chosen.
The leng h o he kinema ic n-link was compa ed o he diame e o he p e ious (n
− 1) link’s d i e uni , o in he case o he i s link, he end-e ec o leng h was used. I he
leng h o he n-link exceeds he size o he d i e uni (o end-e ec o ) size by mo e han a
ac o o ou , we conside ed i long enough o be buil om h ee elemen s bol ed,
welded, o glued oge he . O he wise, he n- h link will be buil om jus one s uc u al
elemen . Figu e 7 shows examples o links designed om one and h ee s uc u al ele-
men s.
Figu e 7. Examples o he n- h link; (a) om one pa , (b) om h ee pa s.
I he link consis s o one piece o ma e ial, kinema ic and dynamic analysis o he
manipula o ’s 3D model is pe o med i s . Wi hin hese analyzes, a 3D model c ea ed on
Figu e 7. Examples o he n- h link; (a) om one pa , (b) om h ee pa s.
I he link consis s o one piece o ma e ial, kinema ic and dynamic analysis o he
manipula o ’s 3D model is pe o med i s . Wi hin hese analyzes, a 3D model c ea ed on
he basis o he p oposed kinema ic s uc u e wi h he smalles possible o e all dimensions
was used. Wi hin his model, he o iginal elemen s we e g adually eplaced by elemen s
designed acco ding o he p ocedu e indica ed in Figu es 5and 6. The da a ob ained om
hese analyses we e hen used in he p elimina y design o he d i e uni loca ed in he
ollowing join (using a modi ied e sion o he D i ePicke so wa e ool [
18
]. Based on he
d i e uni dimensions, ela i e posi ion o he p e ious join , and he espec i e connec ion
dimensions ( langes), a sui able pa ame e ized 3D model was selec ed om he da abase.
The model has i s pa ame e s se app op ia ely o his use case. The nex s ep o he design
was simila o a design s udy in CAD sys em SolidWo ks, which aimed a he dimensional
op imiza ion o he elemen in such a way as o sui bo h in e ms o s eng h and especially
in e ms o maximum de o ma ion, while achie ing he lowes possible weigh . I i is
no possible o ge he desi ed esul s wi h his elemen , ano he candida e 3D model is
selec ed om he da abase as he basis o he n- h elemen and he p ocess is epea ed un il
a sui able solu ion is ound. Then, a collision analysis is pe o med again. The pu pose o
his analysis was o de e mine whe he he model upda e caused no new collision s a es. I
no collisions a e ound, he kinema ic and dynamic analysis is pe o med again, and he
selec ed p elimina y d i e uni is checked. I i is possible o use he o iginally designed
d i e uni o a uni wi h he same connec ion dimensions, i is possible o end he design o
he n- h elemen and con inue wi h he design p ocess o he nex link in he manipula o .
In case i is necessa y o use a d i e uni wi h di e en connec ion dimensions, he design
p ocess needs o be epea ed om he s ep in which he basic shape and dimensions o he
n h elemen we e designed, and he design p ocess is epea ed un il a sui able solu ion
is ound.
The p ocess is simila in he case whe e he n- h link consis s o h ee elemen s. Again,
indi idual analyses and op imiza ion p ocesses a e g adually pe o med, on he basis o
which bo h pa s o he n- h elemen i sel and he d i e uni loca ed in he espec i e join
we e designed.
Rega dless o whe he he n- h link consis s o one o h ee elemen s, he i e a i e
p ocess is cu en ly almos comple ely au oma ed. This was made possible by he exis ence
o he al eady men ioned da abase, in which he necessa y in o ma ion abou he d i e uni s,
end-e ec o s, and o he used elemen s is s o ed. This da abase also con ains pa ame e ized
3D models om which he manipula o s can be assembled. The au oma ed design has
been implemen ed using he SolidWo ks CAD API, which can be used o au oma e he
indi idual p ocesses ou lined in he block diag am in Figu es 5and 6. Cu en ly, he only
p ocess ha is no ully au oma ed is pe o ming he kinema ic and dynamic analyses.
This is a p ocess ha is qui e p oblema ic due o he a ie y o possible se ings and s ill
equi es con ol and possible in e en ions om a human. Ne e heless, e en his pa o
he design o he n- h elemen has been signi ican ly simpli ied and accele a ed hanks o
he au oma ion o da a ans e be ween he design s eps. The p ocess also conside ed he
Appl. Sci. 2022,12, 5897 9 o 14
case ha i will no be possible o comple e he design o he n- h membe o he obo ic a m,
whe he due o he o e loading o he d i e uni s, de o ma ions exceeding he equi ed
le el, o due o collisions. In ha case, he p ocess e u ned o he kinema ic op imiza ion
s ep wi h upda ed op imiza ion pa ame e s.
3. Resul s
The unc ionali y o ou me hos om p e ious chap e was es ed on a case s udy.
The chosen ask is a manipula ion be ween wo indus ial machines. The models o his
wo kspace a e shown in Figu e 8. The manipula ed objec is a cylind ical s eel objec
weigh ing 2.15 kg. The wo kspace en i onmen was bounded by he indus ial machines,
which ac ed as obs acles. The ask ajec o y was de ined by ou a ge poin s, wo on each
machine, which de ine he posi ion and o ien a ion o he manipula ed objec in space. The
d i e uni da abase consis s o compac d i e uni s om Ha monicD i e CanisD i e se ies
and Spinea DS se ies.
Appl. Sci. 2022, 12, 5897 9 o 13
Figu e 8. Task wo kspace; (a) CAD model, (b) model in MATLAB.
This wo kspace has been modeled in MATLAB as an en i onmen o he e alua ion
in he gene ic op imiza ion algo i hm desc ibed in Sec ion 2.1. The ou pu o he gene ic
algo i hm is a 5 DOF manipula o shown in Figu e 9. Fo cla i y, le us call his kinema ic
s uc u e “A”. The ou pu also includes join angle alues h oughou he mo emen .
These alues we e hen used o mo ion analyses in CAD so wa e.
Figu e 9. Op imized kinema ic s uc u e A; (a) schema ic, (b) iew in MATLAB.
As s a ed in p e ious chap e s, he kinema ic s uc u e was used o build a 3D model
o he manipula o wi h he use o he smalles d i e uni s a ailable in he elemen da a-
base. This model was hen used o mo ion analysis o measu e he o ces and o ques
ac ing on d i e uni s and mechanical elemen s in he manipula o . Then he i e a i e p o-
cess om Sec ion 2.2.1 was un o check and op imize he design. The p elimina y design
is shown in Figu e 10.
Figu e 10. Ini ial 3D model o kinema ic s uc u e A.
The design p ocess o he CAD model o he kinema ic s uc u e A ailed in he de-
sign i e a ion o he hi d link due o sys em collisions (Figu e 11). When designing he
Figu e 8. Task wo kspace; (a) CAD model, (b) model in MATLAB.
This wo kspace has been modeled in MATLAB as an en i onmen o he e alua ion
in he gene ic op imiza ion algo i hm desc ibed in Sec ion 2.1. The ou pu o he gene ic
algo i hm is a 5 DOF manipula o shown in Figu e 9. Fo cla i y, le us call his kinema ic
s uc u e “A”. The ou pu also includes join angle alues h oughou he mo emen . These
alues we e hen used o mo ion analyses in CAD so wa e.
Appl. Sci. 2022, 12, 5897 9 o 13
Figu e 8. Task wo kspace; (a) CAD model, (b) model in MATLAB.
This wo kspace has been modeled in MATLAB as an en i onmen o he e alua ion
in he gene ic op imiza ion algo i hm desc ibed in Sec ion 2.1. The ou pu o he gene ic
algo i hm is a 5 DOF manipula o shown in Figu e 9. Fo cla i y, le us call his kinema ic
s uc u e “A”. The ou pu also includes join angle alues h oughou he mo emen .
These alues we e hen used o mo ion analyses in CAD so wa e.
Figu e 9. Op imized kinema ic s uc u e A; (a) schema ic, (b) iew in MATLAB.
As s a ed in p e ious chap e s, he kinema ic s uc u e was used o build a 3D model
o he manipula o wi h he use o he smalles d i e uni s a ailable in he elemen da a-
base. This model was hen used o mo ion analysis o measu e he o ces and o ques
ac ing on d i e uni s and mechanical elemen s in he manipula o . Then he i e a i e p o-
cess om Sec ion 2.2.1 was un o check and op imize he design. The p elimina y design
is shown in Figu e 10.
Figu e 10. Ini ial 3D model o kinema ic s uc u e A.
The design p ocess o he CAD model o he kinema ic s uc u e A ailed in he de-
sign i e a ion o he hi d link due o sys em collisions (Figu e 11). When designing he
Figu e 9. Op imized kinema ic s uc u e A; (a) schema ic, (b) iew in MATLAB.
As s a ed in p e ious chap e s, he kinema ic s uc u e was used o build a 3D model
o he manipula o wi h he use o he smalles d i e uni s a ailable in he elemen da abase.
This model was hen used o mo ion analysis o measu e he o ces and o ques ac ing on