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3-RRR平面并联微动机器人的运动学分析.docx

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3-RRR平面并联微动机器人的运动学分析 Introduction: Theconceptofparallelrobotshasrevolutionizedthefieldofroboticsbyofferinghighprecision,high-speed,andaccuracywhileminimizingdeflectionandfatigue.RRRparallelmanipulatorsarethemostcommonlyusedrobotsintoday'sindustryfortheirflexibilityofimplementationanditssimplekinematics.Thispaperaimstodiscussthekinematicanalysisofa3-RRRparallelrobot. KinematicsAnalysis: The3-RRRparallelrobotisasix-degree-of-freedommechanismthatconsistsofthreelinks,threerevolutejoints,andthreeprismaticjoints.Eachlinkconsistsofacylindricalrodwithoneendconnectedtoarevolutejointandtheotherendconnectedtoaprismaticjoint.Thethreerevolutejointsareconnectedtoacommonfixedbase,andthethreeprismaticjointsareconnectedtoanend-effector.Thelinksareconnectedattheintersectionoftheiraxes,formingatriangularpyramidalframework. Theinversekinematicanalysisofthe3-RRRparallelrobotinvolvesdeterminingthejointanglesthatwillresultinaspecificend-effectorposition.Themathematicalformulationoftheinversekinematicsproblemrevealsthatthereisnoclosed-formsolution.Therefore,theforwardkinematicsofthe3-RRRparallelrobotmustbereviewedinordertodeterminetheend-effectorposition. Theforwardkinematicsanalysisofthe3-RRRparallelrobotdeterminesthepositionandorientationoftheendeffectorbasedonthejointanglesandlinklengths.Thefollowingstepscanbetakeninordertoderivetheforwardkinematicequations: 1.Assignacoordinateframetoeachlink,onefixedtothebaseandtheotherthreeattachedtothecylindricalrods. 2.DerivethetransformationmatricesforeachlinkusingtheDenavit-Hartenbergnotation. 3.Determinethelocationoftheend-effectorinreferencetothebasecoordinateframeusingachainoftransformationsofeachlink. Forthe3-RRRparallelrobot,theforwardkinematicscanbederivedusingthefollowingequations: x=(l2*cos(q1)*cos(q2)+l3*cos(q1)*cos(q2)*cos(q3)+l1*cos(q1)*sin(q2)+l2*cos(q2)*sin(q1)+l3*cos(q3)*sin(q1)*sin(q2))*(l3^2-(l1*sin(q2)+l2*sin(q1))^2)^0.5/((l1*sin(q2)+l2*sin(q1))^2+l3^2*cos(q3)^2)^0.5 y=(l2*cos(q2)*sin(q1)+l3*sin(q1)*sin(q2)*sin(q3)+l1*cos(q2)*sin(