{"id":"https://openalex.org/W2050478952","doi":"https://doi.org/10.1016/s0010-4485(98)00020-7","title":"Variable-feedrate CNC interpolators for constant material removal rates along Pythagorean-hodograph curves","display_name":"Variable-feedrate CNC interpolators for constant material removal rates along Pythagorean-hodograph curves","publication_year":1998,"publication_date":"1998-07-01","ids":{"openalex":"https://openalex.org/W2050478952","doi":"https://doi.org/10.1016/s0010-4485(98)00020-7","mag":"2050478952"},"language":"en","primary_location":{"id":"doi:10.1016/s0010-4485(98)00020-7","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0010-4485(98)00020-7","pdf_url":null,"source":{"id":"https://openalex.org/S4210171473","display_name":"Computer-Aided Design","issn_l":"0010-4485","issn":["0010-4485","1879-2685"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer-Aided Design","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/s0010-4485(98)00020-7","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113609022","display_name":"RidaT. Farouki","orcid":null},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"RidaT. Farouki","raw_affiliation_strings":["Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109, USA","Department of Mechanical Engineering and Applied Mechanics,   University of Michigan, Ann Arbor, MI 48109, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Department of Mechanical Engineering and Applied Mechanics,   University of Michigan, Ann Arbor, MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026013002","display_name":"Jairam Manjunathaiah","orcid":null},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jairam Manjunathaiah","raw_affiliation_strings":["Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109, USA","Department of Mechanical Engineering and Applied Mechanics,   University of Michigan, Ann Arbor, MI 48109, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Department of Mechanical Engineering and Applied Mechanics,   University of Michigan, Ann Arbor, MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069186866","display_name":"David Nicholas","orcid":null},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David Nicholas","raw_affiliation_strings":["Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109, USA","Department of Mechanical Engineering and Applied Mechanics,   University of Michigan, Ann Arbor, MI 48109, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Department of Mechanical Engineering and Applied Mechanics,   University of Michigan, Ann Arbor, MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009942833","display_name":"Guo-Feng Yuan","orcid":null},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Guo-Feng Yuan","raw_affiliation_strings":["Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109, USA","Department of Mechanical Engineering and Applied Mechanics,   University of Michigan, Ann Arbor, MI 48109, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Department of Mechanical Engineering and Applied Mechanics,   University of Michigan, Ann Arbor, MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047942958","display_name":"Sungchul Jee","orcid":"https://orcid.org/0000-0003-0610-0590"},"institutions":[{"id":"https://openalex.org/I89015989","display_name":"Dankook University","ror":"https://ror.org/058pdbn81","country_code":"KR","type":"education","lineage":["https://openalex.org/I89015989"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Sungchul Jee","raw_affiliation_strings":["Department of Mechanical Engineering, Dankook University, 8 Hannam-Dong, Yongsan-Ku, Seoul 140-714, South Korea"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Dankook University, 8 Hannam-Dong, Yongsan-Ku, Seoul 140-714, South Korea","institution_ids":["https://openalex.org/I89015989"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5113609022"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":5.2388,"has_fulltext":false,"cited_by_count":132,"citation_normalized_percentile":{"value":0.95507758,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"30","issue":"8","first_page":"631","last_page":"640"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11159","display_name":"Manufacturing Process and Optimization","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10188","display_name":"Advanced machining processes and optimization","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.6437007188796997},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5727636218070984},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.48622623085975647},{"id":"https://openalex.org/keywords/constant-curvature","display_name":"Constant curvature","score":0.47908955812454224},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4609556496143341},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4546937346458435},{"id":"https://openalex.org/keywords/hodograph","display_name":"Hodograph","score":0.431391179561615},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40059226751327515},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3970152735710144},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30953383445739746},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30368784070014954},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2767924666404724},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2524266839027405}],"concepts":[{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.6437007188796997},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5727636218070984},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.48622623085975647},{"id":"https://openalex.org/C2779668893","wikidata":"https://www.wikidata.org/wiki/Q2250422","display_name":"Constant curvature","level":3,"score":0.47908955812454224},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4609556496143341},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4546937346458435},{"id":"https://openalex.org/C197766306","wikidata":"https://www.wikidata.org/wiki/Q1546281","display_name":"Hodograph","level":2,"score":0.431391179561615},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40059226751327515},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3970152735710144},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30953383445739746},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30368784070014954},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2767924666404724},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2524266839027405},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0010-4485(98)00020-7","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0010-4485(98)00020-7","pdf_url":null,"source":{"id":"https://openalex.org/S4210171473","display_name":"Computer-Aided Design","issn_l":"0010-4485","issn":["0010-4485","1879-2685"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer-Aided Design","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/s0010-4485(98)00020-7","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0010-4485(98)00020-7","pdf_url":null,"source":{"id":"https://openalex.org/S4210171473","display_name":"Computer-Aided Design","issn_l":"0010-4485","issn":["0010-4485","1879-2685"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer-Aided Design","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W77718271","https://openalex.org/W1566743610","https://openalex.org/W1586317938","https://openalex.org/W1912626370","https://openalex.org/W1972335068","https://openalex.org/W1987960041","https://openalex.org/W1990195556","https://openalex.org/W1998916693","https://openalex.org/W2007688905","https://openalex.org/W2010636443","https://openalex.org/W2011266087","https://openalex.org/W2022994234","https://openalex.org/W2023413246","https://openalex.org/W2034121399","https://openalex.org/W2047137744","https://openalex.org/W2050066249","https://openalex.org/W2052315621","https://openalex.org/W2077088715","https://openalex.org/W2078186623","https://openalex.org/W2081468593","https://openalex.org/W2082421519","https://openalex.org/W2090738717","https://openalex.org/W2093207728","https://openalex.org/W2165695530","https://openalex.org/W2181776729","https://openalex.org/W2913692918","https://openalex.org/W4240056637","https://openalex.org/W4242804520","https://openalex.org/W6600355687","https://openalex.org/W6652526562","https://openalex.org/W6684587902","https://openalex.org/W6685599697"],"related_works":["https://openalex.org/W4378192042","https://openalex.org/W2068832901","https://openalex.org/W1543700235","https://openalex.org/W3111769232","https://openalex.org/W2344306736","https://openalex.org/W2152432594","https://openalex.org/W2379906893","https://openalex.org/W3046727562","https://openalex.org/W2948699889","https://openalex.org/W2044124817"],"abstract_inverted_index":{"An":[0],"NC":[1],"system":[2],"that":[3,41],"machines":[4],"a":[5,76,128],"curved":[6],"shape":[7],"at":[8],"fixed":[9],"depth":[10],"of":[11,63,78,90],"cut":[12],"experiences":[13],"time-varying":[14],"cutting":[15],"forces":[16],"due":[17],"to":[18,75],"the":[19,58],"\u2018curvature":[20],"effect\u2019\u2014the":[21],"material":[22],"removal":[23],"rate":[24],"is":[25,47,51],"higher":[26],"than":[27],"nominal":[28],"in":[29,34,66,117,122],"concave":[30],"regions,":[31],"and":[32,49,102,121],"lower":[33],"convex":[35],"regions.":[36],"A":[37],"curvature-dependent":[38],"feedrate":[39,111],"function":[40,70],"automatically":[42],"compensates":[43],"for":[44,54,81],"this":[45,69,91],"effect":[46],"formulated,":[48],"it":[50],"shown":[52],"that,":[53],"Pythagorean-hodograph":[55],"(PH)":[56],"curves,":[57],"periodic":[59],"real":[60],"time":[61],"computation":[62],"reference":[64],"points":[65],"accordance":[67],"with":[68,104,127],"can":[71],"be":[72],"analytically":[73],"reduced":[74],"sequence":[77],"root-finding":[79],"problems":[80],"simple":[82],"monotone":[83],"functions.":[84],"Empirical":[85],"results":[86,105],"from":[87,106],"an":[88,95],"implementation":[89],"variable-feedrate":[92],"interpolators":[93],"on":[94],"open-architecture":[96],"CNC":[97],"milling":[98],"machine":[99],"are":[100],"presented":[101],"compared":[103],"fixed-feedrate":[107],"interpolators.":[108],"The":[109],"curvature-compensated":[110],"scheme":[112],"has":[113],"important":[114],"potential":[115],"applications":[116],"ensuring":[118],"part":[119,124],"accuracy":[120],"optimizing":[123],"programs":[125],"consistent":[126],"prescribed":[129],"accuracy.":[130]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}