FORWARD DISPLACEMENT ANALYSIS AND UNCERTAINTY CONFIGURATIONS OF PARALLEL MANIPULATORS WITH A REDUNDANT BRANCH

The effect of adding a redundant branch in terms of reduction of the n umber of assembly modes and elimination of potential uncertainty confi guration types is investigated for a class of parallel manipulators. C onsidered is a broad class that includes all three-branch manipulators where each branch is comprised of a serial arrangement of three main- arm joints supporting a common payload platform through a passive sphe rical branch end joint-group. The addition of a redundant branch effec tively yields a four-branch manipulator class. Considered in particula r is a 3-4 form of the manipulator where two branch ends meet at one p oint on the mobile platform. Symmetric main-arm joint sensing and actu ation (two sensed/acutated main-arm joints per branch) is utilized. Sy nthetic geometry is used to study the number of assembly configuration s of the resulting 3-4 four-branch parallel manipulators. It is presen ted that the number of assembly modes of three-branch parallel manipul ators with passive spherical branch end joints can be reduced by utili zing a redundant branch. It is shown that there exist up to eight and up to four assembly modes when all unsensed joints are revolute and wh en all unsensed joints are prismatic, respectively. Combinations of un sensed prismatic and revolute joints are also investigated. It is dete rmined that there are up to eight and up to four assembly modes when t he unsensed main-arm joint of one of the concurrent branches is prisma tic and when the unsensed joints of both concurrent branches are prism atic joints, respectively. Resolving the potential assembly modes requ ire only the consideration of, at highest, second-order single-variabl e polynomials. In addition, kinematic design considerations allowing r eduction of feasible assembly modes are discussed. The investigation o f potential uncertainty configuration types is based on examining dege neracies of the screw systems formed by wrenches associated with the f orces that the actuated-joints can apply. All linear dependency cases that could potentially cause uncertainties for the class of four-branc h manipulators are identified. It is shown that while significantly re ducing potential uncertainty configuration types, the addition of a re dundant branch number cannot eliminate all potential dependency (uncer tainty) cases completely. For the remaining potential uncertainty conf iguration types, the characteristics of the corresponding unconstraine d instantaneous degrees of freedom are discussed. (C) 1996 John Wiley & Sons, Inc.