Knowledge-based automated mechanical design of a robot manipulator

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 Publishe ’s No e: MDPI s ays neu al wi h ega d o ju isdic ional claims in published maps and ins i u ional a il- ia ions. Copy igh : © 2022 by he au ho s. Licensee MDPI, Basel, Swi ze land. This a icle is an open access a icle dis ibu ed unde he e ms and condi ions o he C ea i e Commons A ibu ion (CC BY) license (h ps:// c ea i ecommons.o g/licenses/by/ 4.0/). 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