This study deals with the function generation synthesis of spherical four bar mechanism for six independent construction parameters φ 0 , ψ 0 , α 1 , α 2 , α 3 , and α 4 by giving six or more design points with respect to the methods that are used in synthesis procedure. Quaternion algebra is used to derive the objective function of spherical four bar mechanism by following some rotational sequences. Three different methods as interpolation approximation, least squares approximation and Chebyshev approximation are used during synthesis procedure. During the consecutive trials in Chebyshev approximation, a new approach is taken to renew the design points φ i by plotting the graph of the objective functions derivative and taking the roots of it as new design points with two boundary points. Separate examples are given for each section and the results are tabulated. Discussions about the study and comparisons between the used methods are given at the end of the study.

In this paper, structural synthesis of serial platform manipulators is considered. Serial platform manipulators are created according to the development of the platforms and closed loops. Also a new structural formula of mobility of parallel Cartesian platform robot manipulators is presented. Structural synthesis of serial platform manipulators with lower and higher kinematic pairs with respect to their structures are also examined. Structural synthesis of parallel Cartesian platform robot manipulators is also introduced. History of structural formulas DOF are presented as a table with equations, authors, years and some commentaries. New and revised methods for structural synthesis of serial platform manipulators and parallel Cartesian platform robot manipulators are illustrated along with examples. Ó 2006 Elsevier Ltd. All rights reserved. Pep.veı gpelcnabkeyyoq pa,one paccvanpbba.ncz ıogpocs cnpyrnypyouo cbynepa gkanaopveyysx vaybgykznopob gockelobaneksyoq cnpyrnyps. Coplaybe gkanaopveyysx vaybgylznopob goclelobanelsyoq cnpyrnyps ocyobaya ya papbbnbb gkanaopv b pavryynsx roynypob. ı pa,one gpelcnabgeya yobaz cnpyrnypyaz aopvyka, a nar;e paccvanpbba.ncz bogpocs cnpyrnypyouo cbynepa gkanaopveyysx vaybgykznopob gockelobaneksyoq cnpyrnyps c ybpobvb b bscobvb gapavb c noxrb ppeybz bx cnpryrnyps. Bcnopbz cnpyrnypys aopvyk cnegeyb golbb;yocnb gpelcnabkeya b bble na,kbws c ypabyeybzvb, aınopavb, uolavb b yeronopsvb roveynapbzvb. Hobse b gepecvonpeyyse venols cnpyrnypyouo cbynepa gkanaopveyysx vaybgykznopob gockelobaneksyoq cnpyrnyps bkk.cnpbpy.ncz papkbxsvb gpbvepavb.

Compared to wire- or link-driven mechanisms, the plate-spring mechanism provided surpassing force transmission, with >14 N force transmission achieved, which enables most laparoscopic surgery with single port access. In addition, the high degree of freedom structure of the proposed design permitted an expanded workspace, which might be the most competitive characteristic among the single port systems reported to date.

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