Waldron, KJ 1976, 'Elimination of the branch problem in graphical burmester mechanism synthesis for four finitely separated positions', Journal of Manufacturing Science and Engineering, Transactions of the ASME, vol. 98, no. 1, pp. 176-182.
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A graphical construction is presented which, when used for Burmester mechanism synthesis for four finitely separated positions, enables the designer to avoid solutions which will not pass all design positions without being disconnected. The construction is applied to the circle point curve and locates all regions of that curve which give acceptahlr solutions. The procedure is simple, requiring only construction of circles and strairhi lines. It is also compatible with Modler's technique for ensuring that the linkage pasxrs the design positions in the desired order. © 1976 by ASME.
In industrial design, the problem of guiding a body through a number of nominated positions frequently arises. It is referred to as the ″plane position problem″ . The basic solution of the plane position problem is due to Burmester and is usually referred to by his name. The classical Burmester procedure has always had a frustrating defect; it produces spurious solutions. Recent work has produced a simple graphical technique for eliminating spurious solutions in the four position problem. It is the purpose of this paper to present a step-by-step graphical design procedure incorporating these developments.
Waldron, KJ 1976, 'GRAPHICAL SOLUTION OF THE BRANCH AND ORDER PROBLEMS OF LINKAGE SYNTHESIS FOR MULTIPLY SEPARATED POSITIONS.', American Society of Mechanical Engineers (Paper), no. 76 -DET-16.
The material presented in this paper permits solution linkages to be located that are free of branch change and progress through design positions in a required order for all finitely separated and multiply separated four-bar Burmester synthesis problems. Since neither the order nor the branch problem applies to infinitesimally separated position problems, it can be said that all four-bar Burmester synthesis cases have been covered. Two examples are demonstrated to indicate the application of graphical solutions.
Equations are developed for the distance between a manipulator link and an obstacle - both being enclosed in surfaces of general form. A linearized form of these equations is also developed for use in step-by-step path calculations. Simplification of the problem by enclosing links and obstacles in envelopes of simple geometry is discussed. A new method by which a link whose envelope contacts that of an obstacle can be guided around the obstacle is also developed.