Synthesis of Spatial Mechanism UR-2SS for Path Generation

This article presents a new spatial mechanism with single degree of freedom (DOF) for three-dimensional path generation. The path can be defined by prescribing at most seven precision points. The moving platform of the mechanism is supported by a U-R (universal-revolute) leg and two S–S (spherical–spherical) legs. The driving unit is the first axis of the universal pair. The U-R leg is synthesized first with the problem of order defects being considered. Precision points then lead to prescribed poses of the moving platform. Two S–S legs are then synthesized to meet these poses. This spatial mechanism with a given input is analogous to a planar kinematic chain so that all possible configurations of the spatial mechanism can be constructed. A strategy consisting of three stages for evaluating branch defects is developed with the aid of the characteristic of double configurations and the technique of coding three constituent four-bar linkages. Two numerical examples are presented to illustrate the design, the evaluation of defects, and the performance of the mechanism.

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Synthesis and analysis of spatial CS-3SS mechanism for body guidance

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406214566034 ◽

2015 ◽

Vol 229 (13) ◽

pp. 2455-2466

Author(s):

Wen-Yeuan Chung

Keyword(s):

Degrees Of Freedom ◽

Three Dimensional ◽

Kinematic Chain ◽

Spherical Joint ◽

Numerical Examples ◽

Spatial Mechanism ◽

Cylindrical Joint ◽

Input Parameters ◽

Three Stages ◽

Moving Platform

This work presents a new spatial mechanism for three-dimensional body guidance. The moving platform of this mechanism is supported by a C–S leg and three S–S legs. Driving unit is the cylindrical joint and has two input parameters. The strategy for synthesizing the C–S leg is proposed and at most eight positions of the spherical joint can be prescribed, while at most seven positions can be prescribed in designing each S–S leg. This CS-3SS mechanism can thus be synthesized by prescribing at most seven precision poses. For this multi-loop spatial mechanism, both noticeable works that are the analysis of configurations and strategy for evaluating branch defects are carried out. The mechanism by giving two inputs has zero degrees of freedom and is analogous to a spherical kinematic chain with five links. At most eight configurations can be obtained and the criterion of double configurations is derived successfully. These results are based on to develop the strategy for evaluating branch defects. This strategy has three stages which are calculating the values of criteria, checking properties of other branches and final verification. Two numerical examples are presented to illustrate the design, the evaluation of defects, and the performance of the proposed mechanism.

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A Method for Detection of Distinct Mechanisms of a Planar Kinematic Chain

Transactions of the Canadian Society for Mechanical Engineering ◽

10.1139/tcsme-1988-0003 ◽

1988 ◽

Vol 12 (1) ◽

pp. 15-20 ◽

Cited By ~ 1

Author(s):

L.K. Patel ◽

A.C. Rao

Keyword(s):

Efficient Method ◽

Numerical Scheme ◽

Kinematic Chain ◽

Degree Of Freedom ◽

Single Degree Of Freedom ◽

Single Degree ◽

A Chain

This paper presents a computationally simple and efficient method for identification of distinct mechanisms of a planar kinematic chain having a single degree of freedom. It is proposed that velocity diagrams for all the inversions of a chain be drawn and the possible isomorphism among these velocity diagrams be detected. From the velocity diagram, a motion transfer point matrix can be prepared resulting in the development of a numerical scheme to be associated with a mechanism. Identical schemes lead to detection of isomorphism between mechanisms. The main advantage of this method is that, apart form detecteing isomorphism, it indicates which of the inversions is better kinematically e.g. higher the total number of vectors, better is the mechanism.

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Kinematic Analysis of Spatial Mechanisms by Means of Screw Coordinates. Part 2—Analysis of Spatial Mechanisms

Journal of Engineering for Industry ◽

10.1115/1.3427919 ◽

1971 ◽

Vol 93 (1) ◽

pp. 67-73 ◽

Cited By ~ 29

Author(s):

M. S. C. Yuan ◽

F. Freudenstein ◽

L. S. Woo

Keyword(s):

Computer Program ◽

Kinematic Analysis ◽

Static Force ◽

Single Degree Of Freedom ◽

Numerical Examples ◽

Spatial Mechanism ◽

Single Degree ◽

Spatial Mechanisms ◽

Torque Analysis ◽

Basic Concepts

The basic concepts of screw coordinates described in Part I are applied to the numerical kinematic analysis of spatial mechanisms. The techniques are illustrated with reference to the displacement, velocity, and static-force-and-torque analysis of a general, single-degree-of-freedom spatial mechanism: a seven-link mechanism with screw pairs (H)7. By specialization the associated computer program is capable of analyzing many other single-loop spatial mechanisms. Numerical examples illustrate the results.

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A New Design Methodology for Planar Vibration Absorbers

Volume 7A: 17th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc99/vib-8214 ◽

1999 ◽

Author(s):

Pat Blanchet ◽

Harvey Lipkin

Keyword(s):

Design Methodology ◽

Exciting Force ◽

Degree Of Freedom ◽

Vibration Absorbers ◽

Specific Design ◽

Single Degree Of Freedom ◽

Numerical Examples ◽

Single Degree ◽

Planar Vibration ◽

Design Freedom

Abstract A new methodology is presented for the design of planar vibration absorbers. For the most part, previous methods have dealt with systems constrained to a single degree-of-freedom and require the absorber to be along the line of the exciting force. The presented methodology is more versatile and allows the placement of the absorber as a design freedom. Three specific design techniques for force and couple excitations are detailed along with numerical examples illustrating the results.

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The Design of a Single Degree of Freedom Open-Loop Spatial Mechanism That Incorporates Geared Connections

Volume 4: Design and Manufacturing ◽

10.1115/imece2009-12806 ◽

2009 ◽

Cited By ~ 1

Author(s):

Joseph M. Bari ◽

Carl D. Crane ◽

David B. Dooner ◽

Javier Roldan Mckinley

Keyword(s):

Numerical Optimization ◽

Closed Loop ◽

Three Dimensional ◽

Open Loop ◽

Degree Of Freedom ◽

Single Degree Of Freedom ◽

Variable Parameters ◽

Spatial Mechanism ◽

Repetitive Tasks ◽

Position And Orientation

A means has been discovered to apply gear pairing to create a one degree of freedom open-loop spatial mechanism. A specially chosen geometry consisting of three pairs of parallel joint axes is constricted by five sets of gears, three of which are parallel planar, allows for a reconfigurable mechanism that is suited for repetitive tasks. Previous work has examined three-dimensional rigid body guidance in closed-loop geared mechanisms, but has not come to a solution for the open-loop case. Gear pairs are designed based upon a desired position and orientation path for the end effector. Numerical optimization is performed to obtain physically realizable gear profiles. Non-circular gear centrodes must be continuous and smooth as well as mono-directional, that is, gear ratios of a given pair may not switch signs. These constraints eliminate non-realizable or non-optimal gears in favor of simple, more easily produced profiles. Variable parameters include link lengths, joint offsets and twist angles. Numerical examples are presented.

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Rigidly Foldable Thick Origami Using Designed-Offset Linkages

Journal of Mechanisms and Robotics ◽

10.1115/1.4045940 ◽

2020 ◽

Vol 12 (2) ◽

Cited By ~ 1

Author(s):

Robert J. Lang ◽

Nathan Brown ◽

Brian Ignaut ◽

Spencer Magleby ◽

Larry Howell

Keyword(s):

Plate Thickness ◽

Degree Of Freedom ◽

Unique Combination ◽

Single Degree Of Freedom ◽

Spatial Mechanism ◽

Single Degree ◽

Unfolded State ◽

The Individual ◽

Kinematic Motion

Abstract We present new families of thick origami mechanisms that achieve rigid foldability and parallel stacking of panels in the flat-folded state using linkages for some or all of the hinges between panels. A degree-four vertex results in a multiloop eight-bar spatial mechanism that can be analyzed as separate linkages. The individual linkages are designed so that they introduce offsets perpendicular to the panels that are mutually compatible around each vertex. This family of mechanisms offers the unique combination of planar unfolded state, parallel-stacked panels in the flat-folded state and kinematic single-degree-of-freedom motion from the flat-unfolded to the flat-folded state. The paper develops the mathematics defining the necessary offsets, beginning with a symmetric bird’s-foot vertex, and then shows that the joints can be developed for asymmetric flat-foldable systems. Although in the general case there is no guarantee of achieving perfect kinematic motion, we show that for many cases of interest, the deviation is a tiny fraction of the plate thickness. Mechanical realizations of several examples are presented.

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Design of Cylindrical and Axisymmetric Origami Structures Based on Generalized Miura-Ori Cell

Journal of Mechanisms and Robotics ◽

10.1115/1.4043800 ◽

2019 ◽

Vol 11 (5) ◽

Cited By ~ 2

Author(s):

Yucai Hu ◽

Haiyi Liang ◽

Huiling Duan

Keyword(s):

Three Dimensional ◽

Design Methods ◽

Geometric Design ◽

Degree Of Freedom ◽

Single Degree Of Freedom ◽

Single Degree ◽

Flat Sheet ◽

Folded Structure

Origami has shown its potential in designing a three-dimensional folded structure from a flat sheet of material. In this paper, we present geometric design methods to construct cylindrical and axisymmetric origami structures that can fit between two given surfaces. Due to the symmetry of the structures, a strip of folds based on the generalized Miura-ori cells is first constructed and then replicated longitudinally/circumferentially to form the cylindrical/axisymmetric origami structures. In both designs, algorithms are presented to ensure that all vertexes are either on or strictly within the region between the target surfaces. The conditions of flat-foldability and developability are fulfilled at the inner vertexes and the designs are rigid-foldable with a single degree-of-freedom. The methods for cylindrical and axisymmetric designs are similar in implementation and of potential in designing origami structures for engineering purposes, such as foldcores, foldable shelters, and metamaterials.

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Rigidly Foldable Thick Origami Using Designed-Offset Linkages

Volume 5B: 43rd Mechanisms and Robotics Conference ◽

10.1115/detc2019-97621 ◽

2019 ◽

Cited By ~ 2

Author(s):

Robert J. Lang ◽

Nathan Brown ◽

Brian Ignaut ◽

Spencer Magleby ◽

Larry Howell

Keyword(s):

Degree Of Freedom ◽

Unique Combination ◽

Single Degree Of Freedom ◽

Spatial Mechanism ◽

Single Degree ◽

Unfolded State ◽

The Individual

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Minimum Error Synthesis of Multiloop Plane Mechanisms for Rigid Body Guidance

Journal of Engineering for Industry ◽

10.1115/1.3438283 ◽

1974 ◽

Vol 96 (1) ◽

pp. 107-116 ◽

Cited By ~ 4

Author(s):

K. N. Prasad ◽

C. Bagci

Keyword(s):

Rigid Body ◽

Rigid Bodies ◽

Type I ◽

Path Generation ◽

Relaxation Methods ◽

Single Degree Of Freedom ◽

Minimum Error ◽

Numerical Examples ◽

Single Degree ◽

Matrix Iteration

A variational method of synthesizing single-degree of freedom, single or multiloop plane mechanisms to guide rigid bodies through specified planar positions is presented. The optimum set of dimensions of a mechanism is determined by minimizing an objective function, which is the sum of the squared errors in the generated coordinates of two body points. The design equations are solved either by matrix iteration or Gaussian relaxation methods. By introducing constraints necessary to coincide the two body points, the problem is reduced to that of optimizing a plane mechanism to generate a planar path. Stephenson six-bar mechanism of Type I and the 4R plane mechanism are synthesized for rigid body guidance and path generation. Numerical examples are given, where all the geometric inversions of a mechanism are synthesized as distinct mechanisms, thereby eliminating the mixing of the geometric inversions at the design positions, thus assuring the mobility of the resulting mechanisms within the design interval.

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On the Optimal Shock Isolation of a System with One and a Half Degrees of Freedom

Shock and Vibration ◽

10.1155/1999/492345 ◽

1999 ◽

Vol 6 (4) ◽

pp. 159-167

Author(s):

D.V. Balandin ◽

N.N. Bolotnik ◽

W.D. Pilkey

Keyword(s):

Degrees Of Freedom ◽

Degree Of Freedom ◽

Single Degree Of Freedom ◽

Numerical Examples ◽

Single Degree ◽

Shock Isolation

The limiting performance of shock isolation of a system with one and a half degrees of freedom is studied. The possibility of using a single-degree-of-freedom model for this analysis is investigated. The error of such an approximation is estimated. Numerical examples are presented.

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