A CAD-based hierarchical approach to interference detection among fixture modules in a reconfigurable fixturing system.pdf

pergamon robotics horizontal support locator horizon tal clamp and vertical clamp the robot retrieves a number of vertical supports from the fixture magazine and places these modules on the electromagnetic chuck the robot proceeds to adjust the heights of these modules these fixture modules support the workpiece at the required height the electromagnetic chuck is switched on before any adjustments are to take place thus the position of the fixture module is not affected by the robot end effector exerting force on it during adjustments next a number of horizontal supports are placed on the chuck these are usually placed where they would be in contact with the workpiece robotics two fixture points in the second plane and generally perpendicular to the first plane two horizontal supports and one fixture point in the third plane and generally perpendicular to the first and second planes one horizontal support if holes or locating tabs are used as fixture points the number of fixture modules required to locate the workpiece may be reduced these is a total of 12 linear and rotational movements along the x y and z axes including both positive and negative directions associated with a rigid body in space it must be pointed out that the 3 2 1 rule allows locating of a convex polyhedral workpiece i e prismatic work piece with orthogonal locating planes using the minimum number of fixture points usually the vertical and horizontal supports restrict at least 9 movements out of 12 with the remaining 3 possible movements being constrained by the clamps once the support fixture modules are positioned on the fixture bed the robot proceeds to place the workpiece within this initial fixture layout a number of horizontal clamps and vertical clamps are then placed on the chuck the robot adjusts the height of these modules and activates the clamping mechan isms and thereby fixturing the workpiece into the desired position and orientation figure 2 shows examples of fixtured workpieces the robot may now perform the subsequent assembly operations on the workpiece it must be emphasized that in an industrial environment the clamps must be designed to incorporate a tilt back or turn away cap ability to allow loading and unloading of the workpiece without removal of the clamps fixture module location determination an important objective of a reconfigurable fixturing system is to provide means for a rapid fixture design analysis and a valid robot program that is generated automatically therefore a fixture design and analysis system has been developed consisting of the six program modules pre processor design analysis verification interference detection and post processor the system 21 allows the fixture layout design i e specification of the fixture contact point on the 3 d model of the workpiece analysis and verification to be performed interactively in a computer aided design cad environment the information provided to the interference detection module consists of the locations of the reference frames of the fixture modules with respect to the assembly station coordinate frame all tool center point tcp locations for robot movements are determined by translation and rotation transforma interference detection among fixture modules b shirinzadeh 43 contact surface flat adjustment k i place the height base fact height adj pic eking arms s urfac shaft a b oamping trigger clal clamping release trig t adjustmc no contact plun shaft c d fig 1 schematic diagram of a vertical support b horizontal support c vertical clamp and d horizontal clamp tions of the reference frame position on the fixture modules the positioning and orientating of the fixture module are performed in 4 d space three to position and one to orient thus only rotation about the z axis is required to orient the fixture module on the fixture bed in x y plane the following expression decribes the nomenclature for the location description of fixture modules hcf9 module type position frame designation x r z i o o j station 1 therefore the location of reference frame for in this case a horizontal clamp retrieved from the design and verification programs and passed on to the 44 robotics minimum separation maximum separa tion and model boundary and these are carried out sequentially the underlying reason for minimum and maximum separation tests is to create a minimum region in which interference will occur and a maximum region in which interference will not occur regardless of the orientation of the fixture modules as shown in fig 4 the model boundary test is performed if the condition for minimum separation is met and the condition for maximum separation is not thus taking into account the orientation of the fixture modules the strategy and 45 mathematical formulations for each test will be outlined using examples of cases involving inter ferenee between vertical and horizontal supports cases of interference detection involving vertical and horizontal clamps follow similar hierarchical struc ture and formulations minimum separation between vertical supports the test for minimum separation determines if the distance between the axes of the pick place adjust ment coordinate frames of the two vertical supports are smaller than the minimum distance required such that the bases of the two vertical supports would not interfere with each other thus if this condition is not satisfied regardless of the orientation of the fixture modules the two vertical supports will collide during fixture set up figure 5 shows the schematic diagram of two vertical supports located such that the axes through their trigger mechanisms are parallel the geometrical constraint may be for mulated mathematically as follows ace flvs flvs 9 or zmin acc 2flvs 0 10 where flvs is the minimum separation radius for the base signature of the vertical support is the clearance between the two supports and ace is the distance between the pick place locations i e centre to centre on the fixture modules and can be obtained using the following expression ac c vspxi vspxj 2 vspri vsprj 2 11 where vsp signifies the pick place reference location on the vertical support with respect to the fixture bed coordinate frame for i and j vertical supports if the above condition is not met it can be concluded that the two vertical supports will interfere with each other regardless of their orientation on the fixture bed therefore there is no need to follow through with the rest of the analysis for the vertical supports in question however if the geometrical constraint for minimum separation is met then the test for maximum separation is performed maximum separation between vertical supports the test for maximum separation determines if the distance between two vertical supports is larger than the minimum safe distance between the two fixture modules before the orientation setting starts to play a role in the interference detection if the test for maximum separation yields true it can be concluded that the two vertical supports will not collide during fixture set up and the analysis may be terminated in this case if the maximum radius 46 azh robotics g fig 4 concept of minimum and maximum regions for the base signature 2 13vs acc fig 5 schematic diagram of the minimum separation test for two vertical supports acc yc o 6vs 12 t or gmax acc tc o tsvs 0 13 where acc is again the distance between the coordinate frames of the tool application on the two vertical supports tc o is the diagonal distance modules b shirinzadeh 47 from the coordinate axis of the end effector to the comer of the jaws when the jaws are open and 6vs is the distance from the center of the vertical support to the comer of the zero trigger level of the fixture module however if the above geometrical constraint is not met then model boundary test must be performed since the two vertical supports may be positioned such that the interference free assembly may or may not succeed depending on the orientation of the fixture modules with respect to each other table 1 shows the minimum and maximum separation tests for vertical support against horizontal support and horizontal support against horizontal support again in the case of the minimum separation the base signatures are used as the geometrical con straints while in the case of maximum separation for the horizontal support the gripper signature with respect to the fixture module s datum is used as the geometrical constraint during the adjustment operations this provides for larger signature than the gripper signature during the placement operation as shown in table 1 interference formulation between convex polyhedral objects a solid modeling cad i e prime medusa cad package system is used as a platform for the design and analysis of the fixture layout the models of the various fixture modules and workstation have been created and are resident in the cad database the major components of the workstation include the workpiece the robot the magnetic chuck and the gripper however for the purpose of interference detection in the designed fixture layout only the fixture modules and the gripper are used in the analysis the objects are represented by clusters of convex polyhedral models a boundary representa tion b rep scheme is employed to describe each polyhedral model providing a description of the topology and a specification of dimensions the b rep format is also used to transfer data from the cad database to the design and analysis software i acc side view fig 6 vertical supports and the ond offeetor during zero adjustment operation top view 48 robotics j and it must be noted that the fixture designer must select the value for clearance p based on the accuracy of the robot and the application as an example consider the two polyhedral objects shown in fig 8 where na denotes the outward normal for faces i 1 6 and vsj denotes the vertices j l 8 for the object b thus the above formulation which stems from the substitution of components of a vertex of object b into general equation of the face on object a determines which side of the face the vertex in question resides it can be seen that for vertex 1 belonging to object b to be inside the region bounded by the faces 1 6 of object a the solution to the set of equations resulting from the formulation must all be less than zero in other words the following relationships must hold l ii 1 nalxvblx nalyl blr nal vbl ca1 0 1 2 1 na2 vb x q na2yvb y na2 vs ca2 0 15 li6 1 na6xvbi x na6yvbly na6zvbt z ca6 i e the vertex is not bounded by the faces however if the constraints to the set of equations are not satisfied i e 1 ii j 0 i of the fixture modules i and terminate i iyes t t perform required perform maximum operation similar m separation to the above test te re ce detec e i report status tie type yes examine location etc 0 of the fixture modules and terminate no form interference formulation on fixture modules as convex polyhedral objects intertl rence detected report status ie type lno examine location etc l i u of the fixture modules and terminate i yes 11 no interference detected report status of the fixture modules and terminate determine datum points on the base signature for the fixture modules determine the distance between the datum points i remeve convex polyhedral models of the two fixture modules perform transformatiot on the models ie determine the new i itions of the vertices tor fixture modules and gripper determine the face normals outward for i the fixture module and i the gtspper models i pertbrm the interference calculations for various critical locations on the fixture modules j fig 10 software structure for the interference analysis the above sequence for interference detection is followed in conjunction with the procedure and mathematical formulations described in the pre vious sections therefore a minimum separation test is performed first if there exists interference between the fixture modules then it is reported logged and the software selects the next fixture module for analysis if there exists no interference then the maximum separation test is performed if the constraint for maximum separation is met then the outcome is reported logged and again continuing on to the next fixture module however if the maximum separation is not satisfied then the convex polyhedral models of the fixture modules are retrieved from the database and transformed to the designated locations and the detailed model boundary analysis is carried out figure 10 shows a schematic diagram of the software stucture upon completion of the inter ference analysis a worksheet illustrating the 52 robotics fixtures for small batch production mfg engng 41 43 1984 13 latombe j laugier c lefebvre j mazer e miribel j the lm robot programming system in robotics research the second international sympo sium 1985 pp 377 391 14 markus a ruttkay zs vancza j automating fixture design from imitating practice to understand ing principles comput industry 14 99 108 1990 interference detection among fixture modules b shirinzadeh 53 15 nnaji b o lyu p rules for an expert fixturing system on a cad screen using flexible fixtures j intel mfg 1 31 48 1990 16 owens j robot simulation seeing the whole picture indust robot 18 4 10 12 1991 17 pham d t lazaro a autofix an expert cad system for jigs and fixtures j machine tools mfg 30 3 403