HOW TO INVESTIGATE CONSTRAINTS AND MOTIONS IN ASSEMBLIES BY SCREW THEORY

The use of the screw theory to do constraint analysis is described. Screw theory uses a matrix representation to describe, for any mating features, the part's degrees of freedom (twist-matrix) and the directions along which the constraint reacts (wrench-matrix). From these screw-matrices it is possible to individuate the exact constraint conditions of parts into the assembly. Starting from the basics of this theory, how to get screw parameters (constrained directions and degrees of freedom) from screw-matrices is analyzed and how to make the constraint analysis for several serial and parallel constraint configurations is described. Finally, a MATLAB algorithm to analyze possible constraints and motions in assemblies with any complexity is presented.

[1]  D. E. Whitney,et al.  Systematic evaluation of constraint properties of datum flow chain , 2001, Proceedings of the 2001 IEEE International Symposium on Assembly and Task Planning (ISATP2001). Assembly and Disassembly in the Twenty-first Century. (Cat. No.01TH8560).

[2]  Herman Bruyninckx,et al.  Kinematic models for robot compliant motion with identification of uncertainties , 1995 .

[3]  D. E. Whitney,et al.  Application of screw theory to motion analysis of assemblies of rigid parts , 1999, Proceedings of the 1999 IEEE International Symposium on Assembly and Task Planning (ISATP'99) (Cat. No.99TH8470).

[4]  S. Gruber,et al.  Robot hands and the mechanics of manipulation , 1987, Proceedings of the IEEE.

[5]  Daniel E. Whitney,et al.  The Datum Flow Chain: A systematic approach to assembly design and modeling , 1998 .

[6]  D. E. Whitney,et al.  Designing Assemblies , 1999 .

[7]  K. Waldron.  The constraint analysis of mechanisms , 1966 .

[8]  J.D. Adams,et al.  Application of screw theory to constraint analysis of assemblies of rigid parts , 1999, Proceedings of the 1999 IEEE International Symposium on Assembly and Task Planning (ISATP'99) (Cat. No.99TH8470).

[9]  J.Eddie Baker,et al.  Screw system algebra applied to special linkage configurations , 1980 .

[10]  Chi-Haur Wu,et al.  Modeling of Part-Mating Strategies for Automating Assembly Operations for Robots , 1994, IEEE Trans. Syst. Man Cybern. Syst..

[11]  Gaurav Shukla.  Augmenting Datum Flow Chain method to support the top-down design process for mechanical assemblies , 2001 .

[12]  T. Davies.  Kirchhoff's circulation law applied to multi-loop kinematic chains , 1981 .

[13]  R. Konkar,et al.  Incremental Kinematic Analysis of Mechanisms , 1995 .

[14]  Jeffrey D. Adams.  Feature based analysis of selective limited motion in assemblies , 1998 .