A trajectory optimization method for improved tracking of motion commands using CNC machines that experience unwanted vibration
This paper presents a trajectory optimization method for minimizing tracking errors in CNC machines that experience unwanted vibration. The motion command sent to the machine is parameterized using B-splines whose basis functions are filtered using a model of the machine's dynamics. The control...
        Saved in:
      
    
          | Published in | CIRP annals Vol. 65; no. 1; pp. 373 - 376 | 
|---|---|
| Main Authors | , , | 
| Format | Journal Article | 
| Language | English | 
| Published | 
            Elsevier Ltd
    
        2016
     | 
| Subjects | |
| Online Access | Get full text | 
| ISSN | 0007-8506 | 
| DOI | 10.1016/j.cirp.2016.04.100 | 
Cover
| Abstract | This paper presents a trajectory optimization method for minimizing tracking errors in CNC machines that experience unwanted vibration. The motion command sent to the machine is parameterized using B-splines whose basis functions are filtered using a model of the machine's dynamics. The control points associated with the filtered basis functions are then selected to minimize tracking errors subject to the kinematic limits of the machine. The proposed method is shown to be very systematic and easy to use, and it does not sacrifice tracking speed. Experiments are used to demonstrate its superior performance compared to an existing method. | 
    
|---|---|
| AbstractList | This paper presents a trajectory optimization method for minimizing tracking errors in CNC machines that experience unwanted vibration. The motion command sent to the machine is parameterized using B-splines whose basis functions are filtered using a model of the machine's dynamics. The control points associated with the filtered basis functions are then selected to minimize tracking errors subject to the kinematic limits of the machine. The proposed method is shown to be very systematic and easy to use, and it does not sacrifice tracking speed. Experiments are used to demonstrate its superior performance compared to an existing method. | 
    
| Author | Okwudire, C. Duan, M. Ramani, K.  | 
    
| Author_xml | – sequence: 1 givenname: C. surname: Okwudire fullname: Okwudire, C. email: okwudire@umich.edu – sequence: 2 givenname: K. surname: Ramani fullname: Ramani, K. – sequence: 3 givenname: M. surname: Duan fullname: Duan, M.  | 
    
| BookMark | eNp9kU1PAyEQhjloolb_gCeOXlqHZZfdJl5M41fS6KV3QmeppRZYgdaPi39dtvXkoSfI8D4z876ckSPnnSbkksGIARPXqxGa0I2KfB9BmWtwRE4BoB42FYgTchbjCqCqoC5Oyc8tTUGtNCYfvqjvkrHmWyXjHbU6LX1LFz5QY7vgt7rttfhm3Cv1C2r9TobeWuXaSDexf5g8T6hVuDROR5qWKlH92elgtENNN-5DuZT7bM087Kack-OFWkd98XcOyOz-bjZ5HE5fHp4mt9Mhcs7TsOKsYKrN-wuEeaNKFLwW9VgAaxmU4wKxggaKQjFQ8zFWjAlRMq7mgC0v-YBc7dtmH-8bHZO0JqJer5XTfhMla3hV1Y0oeJY2eykGH2PQC4km7XbN5s1aMpB9zHIl-5hlH7OEMtcgo8U_tAvGqvB1GLrZQzrb3xodZMRdWq0J-Vtk680h_BdLPJyh | 
    
| CitedBy_id | crossref_primary_10_1016_j_compstruc_2018_08_009 crossref_primary_10_1016_j_cirp_2021_04_070 crossref_primary_10_1520_JTE20200159 crossref_primary_10_1016_j_micpro_2022_104629 crossref_primary_10_1007_s00170_022_10789_w crossref_primary_10_3390_app11041665 crossref_primary_10_1007_s00170_019_04732_9 crossref_primary_10_1016_j_ymssp_2023_110368 crossref_primary_10_1016_j_isatra_2020_06_025 crossref_primary_10_1016_j_promfg_2018_10_020 crossref_primary_10_1007_s00170_020_05651_w crossref_primary_10_1080_00207721_2024_2377757 crossref_primary_10_1016_j_addma_2021_102290 crossref_primary_10_1115_1_4042606 crossref_primary_10_1016_j_addma_2024_104378 crossref_primary_10_1016_j_cirp_2017_04_058 crossref_primary_10_1007_s00170_021_07200_5 crossref_primary_10_1016_j_cirp_2024_04_081 crossref_primary_10_1016_j_cirp_2018_03_002 crossref_primary_10_1016_j_jmapro_2021_02_059 crossref_primary_10_1115_1_4044355 crossref_primary_10_1016_j_ijmachtools_2024_104135 crossref_primary_10_1016_j_cirp_2024_04_007 crossref_primary_10_1115_1_4034367 crossref_primary_10_1016_j_mechatronics_2017_09_002 crossref_primary_10_1142_S0219876221500286  | 
    
| Cites_doi | 10.1016/S0890-6955(01)00004-9 10.1016/j.cirp.2015.04.102 10.1016/j.cirp.2012.03.132 10.1016/j.ijmachtools.2014.08.004 10.1016/j.cirp.2007.05.088 10.1016/j.cirp.2009.03.045 10.1016/j.ijmachtools.2015.08.002 10.1016/S0007-8506(07)60707-0 10.1016/j.cirp.2015.04.105 10.1016/S0947-3580(99)70155-X 10.1016/j.cirp.2007.05.087 10.1016/j.cirp.2012.03.135 10.1016/j.cirp.2011.05.010 10.1016/j.ymssp.2007.11.017  | 
    
| ContentType | Journal Article | 
    
| Copyright | 2016 CIRP | 
    
| Copyright_xml | – notice: 2016 CIRP | 
    
| DBID | AAYXX CITATION 7TA 8FD JG9  | 
    
| DOI | 10.1016/j.cirp.2016.04.100 | 
    
| DatabaseName | CrossRef Materials Business File Technology Research Database Materials Research Database  | 
    
| DatabaseTitle | CrossRef Materials Research Database Technology Research Database Materials Business File  | 
    
| DatabaseTitleList | Materials Research Database  | 
    
| DeliveryMethod | fulltext_linktorsrc | 
    
| Discipline | Engineering | 
    
| EndPage | 376 | 
    
| ExternalDocumentID | 10_1016_j_cirp_2016_04_100 S0007850616301007  | 
    
| GroupedDBID | --K --M .~1 0R~ 1B1 1~. 1~5 29B 4.4 457 4G. 5GY 5VS 7-5 71M 8P~ 9JN AABNK AABXZ AACTN AAEDT AAEDW AAEPC AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABDEX ABMAC ABXDB ABXRA ABYKQ ACDAQ ACGFS ACNNM ACRLP ADBBV ADEZE ADIYS ADMUD ADTZH AEBSH AECPX AEKER AENEX AEZYN AFKWA AFRZQ AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AIEXJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 GBLVA HVGLF HZ~ IHE J1W JJJVA KOM LY7 M41 MAGPM MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RNS ROL RPZ SDF SDG SES SET SPC SSM SST SSZ T5K WUQ ~G- AATTM AAXKI AAYWO AAYXX ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU CITATION EFKBS ~HD 7TA 8FD JG9  | 
    
| ID | FETCH-LOGICAL-c333t-53121ad5066c0b8a4c637679601d10492cc508022a10ab9c51166413ab0cd343 | 
    
| IEDL.DBID | .~1 | 
    
| ISSN | 0007-8506 | 
    
| IngestDate | Sun Sep 28 01:27:46 EDT 2025 Wed Oct 01 05:25:23 EDT 2025 Thu Apr 24 23:04:10 EDT 2025 Fri Feb 23 02:34:57 EST 2024  | 
    
| IsPeerReviewed | true | 
    
| IsScholarly | true | 
    
| Issue | 1 | 
    
| Keywords | Computer numerical control (CNC) Trajectory optimization Vibration  | 
    
| Language | English | 
    
| LinkModel | DirectLink | 
    
| MergedId | FETCHMERGED-LOGICAL-c333t-53121ad5066c0b8a4c637679601d10492cc508022a10ab9c51166413ab0cd343 | 
    
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23  | 
    
| PQID | 1835578623 | 
    
| PQPubID | 23500 | 
    
| PageCount | 4 | 
    
| ParticipantIDs | proquest_miscellaneous_1835578623 crossref_citationtrail_10_1016_j_cirp_2016_04_100 crossref_primary_10_1016_j_cirp_2016_04_100 elsevier_sciencedirect_doi_10_1016_j_cirp_2016_04_100  | 
    
| ProviderPackageCode | CITATION AAYXX  | 
    
| PublicationCentury | 2000 | 
    
| PublicationDate | 2016 2016-00-00 20160101  | 
    
| PublicationDateYYYYMMDD | 2016-01-01 | 
    
| PublicationDate_xml | – year: 2016 text: 2016  | 
    
| PublicationDecade | 2010 | 
    
| PublicationTitle | CIRP annals | 
    
| PublicationYear | 2016 | 
    
| Publisher | Elsevier Ltd | 
    
| Publisher_xml | – name: Elsevier Ltd | 
    
| References | Verl, Frey (bib0120) 2012; 61 Tan, Liu, Wang, Yang (bib0160) 2008; 22 Kamalzadeh, Erkorkmaz (bib0100) 2007; 56 Ast, Braun, Eberhard, Heisel (bib0110) 2007; 56 Richardson, Formenti (bib0155) 1982 Altintas, Verl, Brecher, Uriarte, Pritschow (bib0090) 2011; 60 Sencer, Ishizaki, Shamoto (bib0135) 2015; 64 Duan, Ramani, Okwudire (bib0140) 2015 Symens, van Brussel, Swevers (bib0105) 2004; 53 Yoon, Okwudire (bib0115) 2015; 64 Altintas, Khoshdarregi (bib0130) 2012; 61 Altintas, Okwudire (bib0150) 2009; 58 Yang, Ghasemi, Lu, Okwudire (bib0165) 2015; 98 Erkorkmaz, Altintas (bib0095) 2001; 41 Duan, Okwudire (bib0145) 2015 Singer, Singhose, Seering (bib0125) 1999; 5 Yang, Altintas (bib0170) 2015; 88 Duan (10.1016/j.cirp.2016.04.100_bib0140) 2015 Yang (10.1016/j.cirp.2016.04.100_bib0165) 2015; 98 Singer (10.1016/j.cirp.2016.04.100_bib0125) 1999; 5 Yang (10.1016/j.cirp.2016.04.100_bib0170) 2015; 88 Symens (10.1016/j.cirp.2016.04.100_bib0105) 2004; 53 Erkorkmaz (10.1016/j.cirp.2016.04.100_bib0095) 2001; 41 Ast (10.1016/j.cirp.2016.04.100_bib0110) 2007; 56 Altintas (10.1016/j.cirp.2016.04.100_bib0150) 2009; 58 Altintas (10.1016/j.cirp.2016.04.100_bib0130) 2012; 61 Sencer (10.1016/j.cirp.2016.04.100_bib0135) 2015; 64 Verl (10.1016/j.cirp.2016.04.100_bib0120) 2012; 61 Tan (10.1016/j.cirp.2016.04.100_bib0160) 2008; 22 Yoon (10.1016/j.cirp.2016.04.100_bib0115) 2015; 64 Duan (10.1016/j.cirp.2016.04.100_bib0145) 2015 Richardson (10.1016/j.cirp.2016.04.100_bib0155) 1982 Altintas (10.1016/j.cirp.2016.04.100_bib0090) 2011; 60 Kamalzadeh (10.1016/j.cirp.2016.04.100_bib0100) 2007; 56  | 
    
| References_xml | – volume: 60 start-page: 779 year: 2011 end-page: 796 ident: bib0090 article-title: Machine Tool Feed Drives publication-title: Annals of the CIRP – volume: 56 start-page: 373 year: 2007 end-page: 378 ident: bib0100 article-title: Compensation of Axial Vibrations in Ball Screw Drives publication-title: Annals of the CIRP – volume: 56 start-page: 379 year: 2007 end-page: 382 ident: bib0110 article-title: Adaptronic Vibration Damping for Machine Tools publication-title: Annals of the CIRP – volume: 64 start-page: 369 year: 2015 end-page: 372 ident: bib0135 article-title: High Speed Cornering Strategy with Confined Contour Error and Vibration Suppression for CNC Machine Tools publication-title: Annals of the CIRP – volume: 41 start-page: 1637 year: 2001 end-page: 1658 ident: bib0095 article-title: High Speed CNC System Design. Part III: High Speed Tracking and Contouring Control of Feed Drives publication-title: International Journal of Machine Tools and Manufacture – year: 2015 ident: bib0140 article-title: Tracking Control of Non-minimum Phase Systems Using Filtered Basis Functions: A NURBS-based Approach publication-title: Presented at the ASME 2015 Dynamic Systems and Control Conference (DSCC 2015) – volume: 53 start-page: 321 year: 2004 end-page: 324 ident: bib0105 article-title: Gain-scheduling Control of Machine Tools with Varying Structural Flexibility publication-title: Annals of the CIRP – volume: 64 start-page: 381 year: 2015 end-page: 384 ident: bib0115 article-title: Magnet Assisted Stage for Vibration and Heat Reduction in Wafer Scanning publication-title: Annals of the CIRP – volume: 58 start-page: 335 year: 2009 end-page: 338 ident: bib0150 article-title: Dynamic Stiffness Enhancement of Direct-driven Machine Tools Using Sliding Mode Control with Disturbance Recovery publication-title: Annals of the CIRP – volume: 61 start-page: 335 year: 2012 end-page: 338 ident: bib0130 article-title: Contour Error Control of CNC Machine Tools with Vibration Avoidance publication-title: Annals of the CIRP – volume: 61 start-page: 351 year: 2012 end-page: 354 ident: bib0120 article-title: Improvement of Feed Drive Dynamics by Means of Semi-active Damping publication-title: Annals of the CIRP – volume: 98 start-page: 50 year: 2015 end-page: 60 ident: bib0165 article-title: Pre-compensation of Servo Contour Errors Using a Model Predictive Control Framework publication-title: International Journal of Machine Tools and Manufacture – start-page: 167 year: 1982 end-page: 182 ident: bib0155 article-title: Parameter Estimation from Frequency Response Measurements Using Rational Fraction Polynomials publication-title: Proceedings of the International Modal Analysis Conference – volume: 5 start-page: 208 year: 1999 end-page: 218 ident: bib0125 article-title: Comparison of Filtering Methods for Reducing Residual Vibration publication-title: European Journal of Control – start-page: 1 year: 2015 end-page: 14 ident: bib0145 article-title: Minimum-time Cornering for CNC Machines Using an Optimal Control Method with NURBS Parameterization publication-title: The International Journal of Advanced Manufacturing Technology – volume: 88 start-page: 9 year: 2015 end-page: 23 ident: bib0170 article-title: A Generalized On-line Estimation and Control of Five-axis Contouring Errors of CNC Machine Tools publication-title: International Journal of Machine Tools and Manufacture – volume: 22 start-page: 1055 year: 2008 end-page: 1060 ident: bib0160 article-title: Identification of Modal Parameters of a System with High Damping and Closely Spaced Modes by Combining Continuous Wavelet Transform with Pattern Search publication-title: Mechanical Systems and Signal Processing – start-page: 167 year: 1982 ident: 10.1016/j.cirp.2016.04.100_bib0155 article-title: Parameter Estimation from Frequency Response Measurements Using Rational Fraction Polynomials – volume: 41 start-page: 1637 issue: 11 year: 2001 ident: 10.1016/j.cirp.2016.04.100_bib0095 article-title: High Speed CNC System Design. Part III: High Speed Tracking and Contouring Control of Feed Drives publication-title: International Journal of Machine Tools and Manufacture doi: 10.1016/S0890-6955(01)00004-9 – volume: 64 start-page: 369 year: 2015 ident: 10.1016/j.cirp.2016.04.100_bib0135 article-title: High Speed Cornering Strategy with Confined Contour Error and Vibration Suppression for CNC Machine Tools publication-title: Annals of the CIRP doi: 10.1016/j.cirp.2015.04.102 – volume: 61 start-page: 335 issue: 1 year: 2012 ident: 10.1016/j.cirp.2016.04.100_bib0130 article-title: Contour Error Control of CNC Machine Tools with Vibration Avoidance publication-title: Annals of the CIRP doi: 10.1016/j.cirp.2012.03.132 – volume: 88 start-page: 9 year: 2015 ident: 10.1016/j.cirp.2016.04.100_bib0170 article-title: A Generalized On-line Estimation and Control of Five-axis Contouring Errors of CNC Machine Tools publication-title: International Journal of Machine Tools and Manufacture doi: 10.1016/j.ijmachtools.2014.08.004 – volume: 56 start-page: 379 issue: 1 year: 2007 ident: 10.1016/j.cirp.2016.04.100_bib0110 article-title: Adaptronic Vibration Damping for Machine Tools publication-title: Annals of the CIRP doi: 10.1016/j.cirp.2007.05.088 – volume: 58 start-page: 335 issue: 1 year: 2009 ident: 10.1016/j.cirp.2016.04.100_bib0150 article-title: Dynamic Stiffness Enhancement of Direct-driven Machine Tools Using Sliding Mode Control with Disturbance Recovery publication-title: Annals of the CIRP doi: 10.1016/j.cirp.2009.03.045 – volume: 98 start-page: 50 year: 2015 ident: 10.1016/j.cirp.2016.04.100_bib0165 article-title: Pre-compensation of Servo Contour Errors Using a Model Predictive Control Framework publication-title: International Journal of Machine Tools and Manufacture doi: 10.1016/j.ijmachtools.2015.08.002 – volume: 53 start-page: 321 issue: 1 year: 2004 ident: 10.1016/j.cirp.2016.04.100_bib0105 article-title: Gain-scheduling Control of Machine Tools with Varying Structural Flexibility publication-title: Annals of the CIRP doi: 10.1016/S0007-8506(07)60707-0 – volume: 64 start-page: 381 issue: 1 year: 2015 ident: 10.1016/j.cirp.2016.04.100_bib0115 article-title: Magnet Assisted Stage for Vibration and Heat Reduction in Wafer Scanning publication-title: Annals of the CIRP doi: 10.1016/j.cirp.2015.04.105 – volume: 5 start-page: 208 issue: 2 year: 1999 ident: 10.1016/j.cirp.2016.04.100_bib0125 article-title: Comparison of Filtering Methods for Reducing Residual Vibration publication-title: European Journal of Control doi: 10.1016/S0947-3580(99)70155-X – volume: 56 start-page: 373 issue: 1 year: 2007 ident: 10.1016/j.cirp.2016.04.100_bib0100 article-title: Compensation of Axial Vibrations in Ball Screw Drives publication-title: Annals of the CIRP doi: 10.1016/j.cirp.2007.05.087 – start-page: 1 year: 2015 ident: 10.1016/j.cirp.2016.04.100_bib0145 article-title: Minimum-time Cornering for CNC Machines Using an Optimal Control Method with NURBS Parameterization publication-title: The International Journal of Advanced Manufacturing Technology – year: 2015 ident: 10.1016/j.cirp.2016.04.100_bib0140 article-title: Tracking Control of Non-minimum Phase Systems Using Filtered Basis Functions: A NURBS-based Approach – volume: 61 start-page: 351 issue: 1 year: 2012 ident: 10.1016/j.cirp.2016.04.100_bib0120 article-title: Improvement of Feed Drive Dynamics by Means of Semi-active Damping publication-title: Annals of the CIRP doi: 10.1016/j.cirp.2012.03.135 – volume: 60 start-page: 779 issue: 2 year: 2011 ident: 10.1016/j.cirp.2016.04.100_bib0090 article-title: Machine Tool Feed Drives publication-title: Annals of the CIRP doi: 10.1016/j.cirp.2011.05.010 – volume: 22 start-page: 1055 issue: 5 year: 2008 ident: 10.1016/j.cirp.2016.04.100_bib0160 article-title: Identification of Modal Parameters of a System with High Damping and Closely Spaced Modes by Combining Continuous Wavelet Transform with Pattern Search publication-title: Mechanical Systems and Signal Processing doi: 10.1016/j.ymssp.2007.11.017  | 
    
| SSID | ssj0055072 | 
    
| Score | 2.3501453 | 
    
| Snippet | This paper presents a trajectory optimization method for minimizing tracking errors in CNC machines that experience unwanted vibration. The motion command sent... | 
    
| SourceID | proquest crossref elsevier  | 
    
| SourceType | Aggregation Database Enrichment Source Index Database Publisher  | 
    
| StartPage | 373 | 
    
| SubjectTerms | Basis functions Commands Computer numerical control Computer numerical control (CNC) Kinematics Tracking Tracking errors Trajectory optimization Vibration  | 
    
| Title | A trajectory optimization method for improved tracking of motion commands using CNC machines that experience unwanted vibration | 
    
| URI | https://dx.doi.org/10.1016/j.cirp.2016.04.100 https://www.proquest.com/docview/1835578623  | 
    
| Volume | 65 | 
    
| hasFullText | 1 | 
    
| inHoldings | 1 | 
    
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Baden-Württemberg Complete Freedom Collection (Elsevier) issn: 0007-8506 databaseCode: GBLVA dateStart: 20110101 customDbUrl: isFulltext: true dateEnd: 99991231 titleUrlDefault: https://www.sciencedirect.com omitProxy: true ssIdentifier: ssj0055072 providerName: Elsevier – providerCode: PRVESC databaseName: Elsevier ScienceDirect issn: 0007-8506 databaseCode: .~1 dateStart: 19950101 customDbUrl: isFulltext: true dateEnd: 99991231 titleUrlDefault: https://www.sciencedirect.com omitProxy: true ssIdentifier: ssj0055072 providerName: Elsevier – providerCode: PRVESC databaseName: Elsevier SD Complete Freedom Collection [SCCMFC] issn: 0007-8506 databaseCode: ACRLP dateStart: 19950101 customDbUrl: isFulltext: true dateEnd: 99991231 titleUrlDefault: https://www.sciencedirect.com omitProxy: true ssIdentifier: ssj0055072 providerName: Elsevier – providerCode: PRVESC databaseName: ScienceDirect issn: 0007-8506 databaseCode: AIKHN dateStart: 19950101 customDbUrl: isFulltext: true dateEnd: 99991231 titleUrlDefault: https://www.sciencedirect.com omitProxy: true ssIdentifier: ssj0055072 providerName: Elsevier – providerCode: PRVLSH databaseName: Elsevier Journals issn: 0007-8506 databaseCode: AKRWK dateStart: 19800101 customDbUrl: isFulltext: true mediaType: online dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0055072 providerName: Library Specific Holdings  | 
    
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3PS8MwFA5jXvQg_sT5YzzBm9S1a1LX4yiOqbjThN1Cmra64dqxdYoX_dd9r2mHiuzgsSUJJS_53kv6vu8xdoG4myToWq1EKGGRoJKlPG1bOnISFYXcD23iDj8MvP4jvxuJUY0FFReG0ipL7DeYXqB1-aZVzmZrNh4Txxfdm0B_5OEiNYxyzq-pisHVxyrNg-S6jGK4jWiMrUvijMnx0uNCs9LxSO7UIZbb387pF0wXvqe3w7bLoBG65rt2WS1O99jWNynBffbZhXyuJsUd_DtkCATTkmEJpkg0YHQK4-IKIY6oraZLcsgSMIV8AGdgSrxfoFT4JwgGAUyLTMt4AfmzyiFeqSLDMn0ji0TwSqdt6n7Ahr2bYdC3yuIKlnZdN7dw77UdFeGMoGnCjuLaI2EXPNA4ER7R_LbWouDhKsdWoa8xMPM89HgqtHXkcveQ1dMsjY8YaC9suyLyVacTc40hgAjR_CSMh0Ni-NBgTjWpUpfC41T_4kVWGWYTSYaQZAhpc5JRbrDLVZ-Zkd1Y21pUtpI_Fo9Ev7C233llWIm7in6VqDTOlguJQCcQyzA2PP7n2Cdsk57Mbc0pq-fzZXyG8UseNosF2mQb3dv7_uALD2rw9g | 
    
| linkProvider | Elsevier | 
    
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV07T8MwELaqMgAD4inK85DYUGheDs1YRVQF2k5F6mY5TgKtaFq1KYgF_jp3TlIBQh1YE9uKfPZ3Z-e-7xi7RNxNEnStRsIlN0hQyZCeMg0VWYmMQtcPTeIOd3te-9G9H_BBhQUlF4bSKgvszzFdo3XxpF7MZn06HBLHF90bR3_k4SLVjPI1l9s3dAK7_ljmeZBeVy4ZbiIcY_OCOZMneamhFq20PNI7tYjm9rd3-oXT2vm0ttlWETVCM_-wHVaJ0122-U1LcI99NiGbyZG-hH-HCSLBuKBYQl4lGjA8haG-Q4gjaqvolhwmCeSVfACnYEzEX6Bc-CcIegGMdaplPIfsWWYQL2WRYZG-kUkieKXjNnXfZ_3WbT9oG0V1BUM5jpMZuPlsS0Y4I2ibsCFd5ZGyC55orAjPaL6tFNdEXGmZMvQVRmaehy5PhqaKHNc5YNV0ksaHDJQX2g6PfNloxK7CGICHaH9SxsMhMX6oMaucVKEK5XEqgPEiyhSzkSBDCDKEMF3SUa6xq2Wfaa67sbI1L20lfqwegY5hZb-L0rACtxX9K5FpPFnMBSIdRzDD4PDon2Ofs_V2v9sRnbvewzHboDf51c0Jq2azRXyKwUwWnunF-gWn-vKL | 
    
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+trajectory+optimization+method+for+improved+tracking+of+motion+commands+using+CNC+machines+that+experience+unwanted+vibration&rft.jtitle=CIRP+annals&rft.au=Okwudire%2C+C.&rft.au=Ramani%2C+K.&rft.au=Duan%2C+M.&rft.date=2016&rft.issn=0007-8506&rft.volume=65&rft.issue=1&rft.spage=373&rft.epage=376&rft_id=info:doi/10.1016%2Fj.cirp.2016.04.100&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_cirp_2016_04_100 | 
    
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0007-8506&client=summon | 
    
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0007-8506&client=summon | 
    
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0007-8506&client=summon |