1,720,971 research outputs found
Forward kinematics in polynomial form of the general Stewart platform
No full textThe paper presents a new algorithm to solve, in polynomial form, the forward kinematics of the general-geometry 6-6 fully-parallel manipulator. The forty solutions that the problem at hand admits in the complex domain are found by determining the roots of a 40th-order univariate polynomial equation. Unlike the existing algorithm, the proposed one is suitable for implementation in a standard floating-point computation environment. A numerical example shows application of the new algorithm to a case study
Kinematic clearance sensitivity analysis of spatial structures with revolute joints
No full textThe paper presents a new method to assess the influence of joint clearances in spatial structures that are composed of links connected be revolute joints. The method allows assessment of the amount by which joint clearances affect the rigid-body position of a generic link of the structure when an external load is exerted on the link. Unlike other procedures, the proposed method relies on the clearance-free idealization of the structure under investigation. An example shows application of the proposed method to the analysis of the structure derived from a multi-loop manipulator by freezing its actuators
Direct position analysis in analytical form of the parallel manipulator that features a planar platform supported at six points by six planes
No full textThe paper presents the direct position analysis of the parallel manipulator that features and end-effector with six coplanar spherical joints constrained to lie on x-y sliding tables. By properly controlling the postures of the sliding tables, the end-effector is endowed with up to six degrees of freedom with respect to the frame. The direct position analysis, aimed at determining all positions of the end-effector consistent with a given set of sliding table postures, is solved in analytical form by first devising a system of eight nonlinear compatibility equations in a corresponding number of unknowns. By an original elimination procedure, a final eighth-order univariate polynomial equation is obtained whose eight roots represent as many assembly configurations for the analyzed manipulator. A numerical example is finally reported which confirms the new theoretical results
Managing discontinuity in dynamics
No full textThe paper proposes a method aimed at performing numerical integration of the equations of motion for dynamic systems whose behavior experiences discontinuity. The involved discontinuity can be both acceleration discontinuity and velocity discontinuity. The method is based on a timely detection of discontinuity occurrences and on updating the state matrix for selection of the suited set of motion equations
Recursive determination of conjugate profiles in planar motion with application to gear design
No full textA general procedure for determining the envelope of the outline of planar rigid figures is preseated which allows both local and finite undercutting to be taken into account. A suitable parametrization of the enveloped curves. together with the insertion of cusps wherever undercutting occurs, enables the procedure to be applied recursively while maintaining high accuracy in describing the resulting envelopes. The proposed procedure provides the basis for an original validat ion method regarding parallel-axis spur and helical gears. The method takes into account possible undercutting during hobbing or shaping. considers the desi red amount of meshing clearance over the entire tooth profile. and is able to detect meshing interference. Further, it provides a criterion in choosing the proper cutter profile. A numerical example showing the application of the method is discussed at the end of the paper
Designing Synchronous Belt Transmissions With Variable Velocity Ratio
No full textThe paper presents a new procedure to design a two-pulley synchronous belt transmission connecting, with no belt tensioner, two parallel-axis shafts with a variable velocity ratio. The procedure takes into account the limited number of choices for pitch and length of off-the-shelf synchronous belts, which translates into the need of fine-adjusting either the center distance or the law of motion. Differently from other approaches reported in the technical literature, the suggested method is based on the numerical solution of a set of functional equations. A numerical example shows application of the proposed method to a case study
The Kinematics of Conical Involute Gear Hobbing
No full textThe paper is aimed at finding all relative rigid-body positions of two conical involute gears that mesh together with no backlash. The results are then specialized to determine two key setting parameters for a hobbing machine that has to cut a conical involute gear. A numerical example shows application of the presented results to a case study
Polynomial solution of the spatial burmester problem
No full textThe paper presents a new method for the dimensional synthesis of the spatial guidance linkage that features the guided body connected to the base by the interposition of five rods having spherical joints at both extremities. The linkage is required to index the guided body through seven arbitrarilychosen rigid-body positions. Core of the proposed method is an original algebraic elimination procedure that allows five unknowns to be dropped from a set of six second-order algebraic equations in six unknowns. As a result, a final univariate polynomial equation of twentieth order is obtained whose twenty roots, in the complex domain, represent as many possible placements for a connecting rod. A numerical example is reported
Forward displacement analysis of parallel mechanisms. Closed form solution of PRR-3S and PPR-3S structures
No full textThe forward displacement analysis (FDA) in closed form of two classes of new parallel mechanisms derived from the Stewart Platform Mechanism (SPM) is presented in this paper. These mechanisms, when a set of actuator displacements is given, become multi-loop structures of type PRR-3S and PPR-3S, with P, R and S for prismatic, revolute and spherical pairs, whereas the SPM has the structure RRR-3S. Solving the FDA in closed form means finding all the possible positions and orientations of the output controlled link when a set of actuator displacements is given, or equivalently, finding all possible closures of the corresponding structure. The closed form analysis of the PRR-3S and PPR-3S structures here presented results in algebraic equations in one unknown of degree 16 and 12 respectively. Hence 16 and 12 closures of the corresponding structures can be obtained. Numerical examples confirm these new theoretical results
Exhaustive enumeration of fully parallel kinematic chains
No full textThe direct position analysis of fully-parallel manipulators entails in essence the analysis of fully-parallel kinematic chains that feature two rigid bodies connected to each other via six binary links (legs) through spherical pairs. Some legs may share their endings, thus different leg arrangements are possible. The paper presents an original procedure for identification and exhaustive enumeration of fully-parallel kinematic chains. The enumeration leads to the identification of twenty-one different fully-parallel kinematic chains and provides the frame within which the state of the art in the field of direct position analysis of fully-parallel manipulators - or, more strictly, of fully-parallel kinematic chains - can be conveyed
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