If we look at locating methods, there types of locating surfaces are applied to five basic locating methods and their variations, which may be found in more than 90 percent of fixture design。Figure2 shows the three types of locating surfaces including plane surfaces, concentric internal surfaces (holes) and external profiles .In the application of modular fixtures, the mostly used locating elements (locators) are top locating pins, side locating pins (or mandrels) and V-blocks. The basic locating methods are 3-plane locating(3-2-1),1-plane and 2-holes locating, mandrel locating, V-pad locating and V-block locating (Fig.3).

There are two types of modular fixturing  systems，i.e., T-slot based and dowel-pin based systems. The former is easier to adjust in assembly, and the latter is better in accuracy, rigidity, manufacturing cost and less demand for the assembly skill [4].In a dowel-pin fixturing system, all fixture elements are positioned and linked together on a baseplate with accurate spacing between adjacent holes. These holes are evenly distributed with accuracy so that once a fixture element is placed on the baseplate with pins, it is clear where the element exactly is and how far it is from the edges of the baseplate or other elements. This makes the fixturing process much easier and makes the design    of fixtures more accurate. With its fixed coordinate locating points, a dowel-pin fixturing system is ideally suitable for applications in CAFD and CNC machining, as well as for robot assembly.

 sketches a dowel-pin type modular fixturing system which includes a library of a large number of standard fixture elements[19].With combinations of the fixture elements, an experiences fixture design can build fixtures for a variety of workpieces. In order to automatically generate a fixture configuration design, the issues for the following problems are presented in the following sections:

(1) the selection of suitable fixture elements and combinations of these elements into desired functional units;

(2) The methodology to mount (position) the fixture units (or elements) in appropriate position and orientations on a baseplate without interference with the space already occupied by the workpiece, machining envelope or other fixture units mounted in advance.

  It should be noted that kinematic constraints, locating accuracy, fixturing stability, and fixturing deformation are also important in fixture planning and fixture configuration design. Once a fixture configuration design is finished , the design performances need to be verified, which are not presented in this paper . Verification results are the feedback information to the fixture configuration design module for alternative designs, if necessary.

3   Analysis of Modular Fixture Structures

Fixturing features of a workpiece have been analyzed , including geometric, operational , and fixturing surface information . Once a fixture structure is decomposed into functional units, fixture elements, and functional surfaces, the fixture design process becomes a search for a match between the fixturing features , a fixture element assembly relationship database is built up based on the analysis of the fixture structure.

Decomposition of Modular Fixture Structure.

The advantage of modular fixture is its adaptability for various workpieces by changing the configuration combinations of fixture elements. Modular fixture structures can be decomposed into: functional untis, elements, and functional surfaces.

      By applying Set Theory, a fixture body can be defined as a set or an assembly of fixture elements. Let F denote a fixture and  （i=1,2,….., ）a fixture element in F, where   is the number of fixture elements in F, i.e. .

                             F={  }                           (1)