Solution intervals for variables in spatial RCRCR linkages

© 2019. ElsevierAn analytic method to compute the solution intervals for the input variables of spatial RCRCR linkages and their inversions is presented. The input-output equation is formulated as the intersection of a single ellipse with a parameterized family of ellipses, both related with the possible values that certain dual angles determined by the configuration of the mechanism can take. Bounds for the angles of the input pairs of the RCRCR and RRCRC inversions are found by imposing the tangency of two ellipses, what reduces to analyzing the discriminant of a fourth degree polynomial. The bounds for the input pair of the RCRRC inversion is found as the intersection of a single ellipse with the envelope of the parameterized family of ellipses. The method provides the bounds of each of the assembly modes of the mechanism as well as the local extrema that may exist for the input variablePeer ReviewedPostprint (author's final draft

Noncircular rolling joints for vibrational reduction in slewing maneuvers

A rolling joint is provided for obtaining slewing maneuvers for various apparatus including space structures, space vehicles, robotic manipulators, and simulators. Two noncircular cylinders, namely a drive and a driven cylinder, are provided in driving contact with one another. This contact is maintained by two pairs of generally S-shaped bands, each pair forming a generally 8-shaped coupling tightly about the circumferential periphery of the noncircular drive and driven cylinders. A stationarily fixed arm extends between and is rotatably journalled with a drive axle and a spindle axle respectively extending through selected rotational points of the drive cylinder and of the driven cylinder. The noncircular cylinders are profiled to obtain the desired varying gear ratio. The novelty of the present invention resides in using specifically profiled noncircular cylinders to obtain a desired varying gear ratio

Synthesis of Spherical 4R Mechanism for Path Generation using Differential Evolution

The problem of path generation for the spherical 4R mechanism is solved using the Differential Evolution algorithm (DE). Formulas for the spherical geodesics are employed in order to obtain the parametric equation for the generated trajectory. Direct optimization of the objective function gives the solution to the path generation task without prescribed timing. Therefore, there is no need to separate this task into two stages to make the optimization. Moreover, the order defect problem can be solved without difficulty by means of manipulations of the individuals in the DE algorithm. Two examples of optimum synthesis showing the simplicity and effectiveness of this approach are included.Comment: Submitted to Mechanism and Machine Theor

The kinematics and vibration of planar linkage mechanisms

PhD ThesisThis thesis reports an investigation into three problems encountered in the design of linkage mechanisms, namely kinematic synthesis, balancing of inertia forces and vibration analysis. A general method of synthesizing planar linkages with pin and sliding joints using an Optimization approach has been investigated. A concise but easily interpreted technique for prescribing the topology of linkages formed by connecting pairs of links together has been developed. The displacement analysis of a linkage is achieved using a direct method which is considerably faster than alternative techniques. A nonlinear optimization algorithm has been modified to cater for non-linear constraints such as transmission angle. These techniques have been incorporated into a computer program. Two case-studies of using the program are given. The first is the synthesis of a six-bar linkage for a motorcycle rear suspension such that a constant centre distance is maintained between the chain-wheels as the suspension deflects. The second concerns the modification of two linkages, containing eight and ten links respectively, to give an improved knitting action for a warp-knitting machine. Operating linkages at high speeds can result in rapidly varying forces acting on the frame due to the mass of the moving links. A procedure to determine suitable counterweights to balance these forces has been developed. Since adding the counterweights may double the total mass of the linkage, the links should have minimum mass. If the mass of a link is reduced too far, the link may vibrate and so detrimentally affect the performance of the linkage. Accordingly the final part reports an investigation into the forced vibration, assuming stability, of a 'Uniform, pin-jointed, binary link. The equations of motion are derived and stability boundaries determined. The theoretical predictions are compared with experimental results from the coupler of a four-bar linkage.Science Research Council: Department of Industry

Universality theorems for configuration spaces of planar linkages

We prove realizability theorems for vector-valued polynomial mappings, real-algebraic sets and compact smooth manifolds by moduli spaces of planar linkages. We also establish a relation between universality theorems for moduli spaces of mechanical linkages and projective arrangements.Comment: 45 pages, 15 figures. See also http://www.math.utah.edu/~kapovich/eprints.htm

Structural and kinematic synthesis of overconstrained mechanisms

Thesis (Doctoral)--Izmir Institute of Technology, Mechanical Engineering, Izmir, 2012Includes bibliographical references (leaves: 133-140)Text in English; Abstract: Turkish and Englishxiii, 140 leavesInvestigation on overconstrained mechanisms needs attention especially in the structural synthesis. Knowing overconstrained conditions and including them in the design process will help creating manipulators with less degree of freedom (DoF) and more rigidity. Also this knowledge of overconstrained conditions will clarify concept of mobility of the parallel manipulators. Another subject, kinematic synthesis of overconstrained mechanisms, is important because it will allow describing a function, path, or motion with less DoF less number of joints. The aim of this thesis is to describe a generalized approach for structural synthesis and creation of new overconstrained manipulators and to describe a potentially generalizable approach for function and motion generation synthesis of overconstrained mechanism. Moreover, screw theory is investigated as a mathematical base for defining kinematics of overconstrained mechanisms. Also, overconstrained mechanisms are investigated and generation of new mechanisms is introduced with examples. Some mathematical models for the subspace geometries are given. A method for defining overconstrained simple structural groups is introduced and extended to design of manipulators with examples and solid drawings. Linear approximation and least squares approximation methods are used for the function generation and motion generation of overconstrained 6R mechanisms. A gap of describing overconstrained manipulators is filled in the area of structural synthesis. A general methodology is described for structural synthesis, mobility and motion calculations of overconstrained manipulators using simple structural groups. A potentially generalizable method for the kinematic synthesis of overconstrained manipulators is described both for function and motion generation