For fixture units , the most important parameter in fixture design is the acting height . Figure 7 shows the acting heights of different fixture units in a fixture design. In general cases, several fixture elements need to be assembled together to achieve the acting height . The acting heights of fixture units are the parameters to know before the suitable fixture elements can be selected. The fixture element selection to form a fixture unit is based on a fixture element assembly relationship analysis as show in the next section.

3.3 Fixture Element  Representation .

    Fixture configuration design is a process of selecting fixture elements from a fixture element library and allocating them together in space according to a certain sequence . In AFCD , a fixture element database needs to be built up , in which the geometry information such as geometric profile , the edges and surfaces of a fixture element is represent in its own(local) coordinate system. To represent the position and orientation of a fixture element in the fixture system, global and local coordinate systems need to be defined . If the global coordinate system which is associated with the fixture baseplate is defined by O (X,Y,Z), the local coordinate system of fixture element   can be defined by three orthogonal unit vectors ( ) with a local origin   ( ) as seen in Fig.8. Once a fixture configuration is built up, the position and orientation of each fixture element needs to be determined. Parameters ( ) are used to represent the position and orientation of the fixture element   in the global coordinate system, where   is the origin of the element local coordinate system and symbol   are the directional cosines of unit vector   and   respectively . The unit vector   is not independent and can be determined by:

During AFCD , the bottom element of a fixture unit is first placed on the fixture baseplate , i.e., the position and orientation of the bottom elements is first determined relative to the global coordinate system , although this relationship may be adjusted later on . Then other fixture elements in the fixture unit are , in turn , allocated until the acting height is reached . This bottom-up approach has been applied to the fixture unit mounting algorithm in the AFCD system.

4 Fixture Configuration Design Examples

Figure 9 shows a fixture configuration design example by using the AFCD system. The input information is extracted from a CAD model of the workpiece with process planning information . Table 1 sketches the input file format . Eight fixture units are generated in the fixture design . The AFCD system provides two kinds of outputs . One is the fixture assembly document which lists the elements used and their positions and orientations . The other is the fixture assembly document. The corresponding fixture assembly drawing are shown without the workpiece in Fig.9(a) and with the workpiece in Fig.9（b）.

Computer-aided modular fixture design is a means to implement flexible fixturing methodology in FMS and CIMS . An automated fixture configuration design (AFCD) system is presented in this paper , which is based on a modular fixture structure analysis. Fixture structure is decomposed into fixture units, elements, and functional surface . MFEARG is developed to represent assembly relationships between fixture elements . Algorithms are developed to automatically search and select fixture elements to form fixture units , mount the units onto a baseplate , and determine spatial positions of each fixture element in the fixture configuration design . The AFCD system can be potentially integrated with a CAPP and NC programming system , which may significantly enhance the flexibity of production systems and reduce the manufacturing planning time.

Acknowledgment