Analytical synthesis of function generating spherical four-bar mechanism for the five precision points Rasim I. Alizade a, * ,O ¨ zgu ¨rKilit b a Department of Mechanical Engineering, Izmir Institute of Technology, Urla, Izmir 35437, Turkey b Mechanical Engineering Department, Faculty of Engineering, Ege University, 35040, Bornova, Izmir, Turkey Received 22 October 2002; received in revised form 10 October 2004; accepted 27 December 2004 Available online 22 February 2005 Abstract Thispaperpresentsananalyticalmethodforsynthesisoffunctiongeneratingspherical4Rmechanisms forthefiveprecisionpoints.Forthedesignrequirementsanadditionalparameter,referencevalueofoutput angle, w 0 ,wasaddedtoangularlinklengthparameters, a i (i =1, ... ,4).Inthedimensionalsynthesisproce- dure,anovelapproachofpolynomialapproximationmethodwasproposedtodeterminethesefivedesign parameters.Usingthismethod,asetoffivenon-linearequationswaseasilytransformedintoasetoffifteen linear equations. Hence, the problem was reduced to the solution of a cubic polynomial equation. More- over, a graphical method in a CAD environment is proposed to verify the solutions. Ó 2005 Elsevier Ltd. All rights reserved. Ó 2005 Elsevier Ltd. All rights reserved. 0094-114X/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechmachtheory.2004.12.010 * Corresponding author. Tel.: +90 232 498 6544; fax: +90 232 498 6505. E-mail addresses: alizada_rasim@hotmail.com (R.I. Alizade), ozgurkilit@mail.ege.edu.tr (O ¨ . Kilit). URLs: http://likya.iyte.edu.tr/mechweb/facultyandstaff/ralizade.htm (R.I. Alizade), http://likya.iyte.edu.tr/mechweb/ facultyandstaff/okilit.htm (O ¨ . Kilit). www.elsevier.com/locate/mechmt Mechanism and Machine Theory 40 (2005) 863–878 Mechanism and Machine Theory