Design of a Bistable Origami Reverse-Fold Using Spherical Kinematics

2017 ◽  
Author(s):  
Rami Alfattani ◽  
Craig Lusk
Keyword(s):  
Change Point ◽  
Design Concept ◽  
Dimensional Synthesis ◽  
Bistable Behavior ◽  
Spherical Mechanisms ◽  
Formal Analogy ◽  
Simple Class ◽  
Parametric Cad ◽  
Position Synthesis ◽  
Spherical Mechanism

This paper presents a new design concept for bistability that can be implemented as a reverse-fold origami mechanism or as a spherical four-bar mechanism. The design is based on the conceptual overlap between a certain simple class of origami mechanisms (the reverse-fold) and a class of spherical change-point mechanisms. Using both a partially compliant spherical mechanism and a piece of origami made with two sheets of paper, we implement the design concept for bistable behavior. The design concept consists in adapting planar two position synthesis to spherical mechanisms and in using a formal analogy between spherical mechanisms and certain simple origami folds. The dimensional synthesis of these two mechanisms is performed using parametric CAD. The design concept was successfully prototyped both as origami and as a partially compliant spherical mechanism.

Singularity-Free RPR and SPS Chains for Actuating Single Degree of Freedom Planar and Spherical Mechanisms

2010 ◽  
Author(s):  
David A. Perkins ◽  
Andrew P. Murray
Keyword(s):  
Reference Frame ◽  
Unique Fixed Point ◽  
Degree Of Freedom ◽  
Moving Frame ◽  
Dimensional Synthesis ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Fixed Frame ◽  
Spherical Mechanisms ◽  
Spherical Mechanism

This paper presents a method of selecting joints relative to a fixed and moving (coupler) frame that can be used to actuate a single degree of freedom planar mechanism using a revolute-prismatic-revolute (RPR) chain or a spherical mechanism via a spherical-prismatic-spherical (SPS) chain. Given a single degree of freedom mechanism, a moving reference frame attached to any link has a motion that can be described with a single parameter. A point relative to this moving frame is sought such that it either continually increases or decreases in distance from a point in the fixed frame over the entire motion. The mechanism can then be moved by placing an actuated prismatic joint between the two points. Moreover, the singularities relative to the joints in the original mechanism are not a concern and the dimensional synthesis can focus on creating the set of circuit-defect free solutions. From this analysis, a unique fixed point is determined relative to two positions and their velocities with the following characteristic. All points in the moving reference frame that are moving away from it in the first position are approaching it in the second position, and vice versa.

A Lamina-Emergent Frustum Using a Bistable Collapsible Compliant Mechanism (BCCM)

2016 ◽  
Author(s):  
Rami Alfattani ◽  
Craig Lusk
Keyword(s):  
Compliant Mechanism ◽  
Dimensional Synthesis ◽  
Bistable Behavior ◽  
Shape Morphing ◽  
Compression Spring ◽  
Parametric Cad ◽  
Design Requirements ◽  
Selection Of

This paper presents a new Bistable Collapsible Compliant Mechanism (BCCM) that is utilized in a Lamina-Emergent Frustum. The mechanism is based on transforming a polygon spiral into spatial frustum shape using a mechanism composed of compliant links and joints that exhibits bistable behavior. A number of mechanism types (graphs) were considered to implement the shape-morphing spiral, including 4-bar, 6-bar, and 8-bar chains. Our design requirements permitted the selection of a particular 8-bar chain as the basis for the BCCM. Bistable behavior was added to the mechanism by introducing a compliant link that functions as a compression spring as the mechanism morphs. Parametric CAD was used to perform the dimensional synthesis. The design was successfully prototyped.

scholarly journals A Lamina-Emergent Frustum Using a Bistable Collapsible Compliant Mechanism

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Rami Alfattani ◽  
Craig Lusk
Keyword(s):  
Compliant Mechanism ◽  
Small Animal ◽  
Solar Still ◽  
Dimensional Synthesis ◽  
Bistable Behavior ◽  
Shape Morphing ◽  
Parametric Cad ◽  
Design Requirements ◽  
Selection Of

This paper presents a new bistable collapsible compliant mechanism (BCCM) that is utilized in a lamina-emergent frustum. The mechanism is based on transforming a polygon spiral into spatial frustum shape using a mechanism composed of compliant links and joints that exhibits a bistable behavior. A number of mechanism types (graphs) were considered to implement the shape-morphing spiral, including 4-bar, 6-bar, and 8-bar chains. Our design requirements permitted the selection of a particular 8-bar chain as the basis for the BCCM. The bistable behavior was added to the mechanism by introducing a snap-through bistability as the mechanism morphs. A parametric CAD was used to perform the dimensional synthesis. The design was successfully prototyped. We anticipate that the mechanism may be useful in commercial small animal enclosures or as a frame for a solar still.

Synthesis of Parallel Manipulator with Single DOF

2013 ◽  
Vol 330 ◽  
pp. 639-643 ◽  
Author(s):  
Chung Huang Yu ◽  
Wen Yeuan Chung
Keyword(s):  
Parallel Manipulator ◽  
Design Concept ◽  
Path Generation ◽  
Dimensional Synthesis ◽  
Type Synthesis ◽  
Numerical Example ◽  
Geometrical Constraints ◽  
Moving Platform ◽  
Manipulator Design

This paper proposed a new manipulator design concept which leads to a single DOF system. The system composed of a moving platform and several supporting legs. It can execute the tasks of 3D body guidance or path generation and thus replace expensive manipulators with high DOF in some conditions. There are mainly two steps in designing this manipulator. The first step is type synthesis to determine the number and types of legs. Dimensional synthesis is then executed based on the movement requirements and geometrical constraints. In this study the reduction of the DOF is also analyzed for various legs added between the moving platform and the ground. A numerical example of executing 3D body guidance is given to verify the proposed new concept.

Geometric Characteristics of the Center-Point Curve Based on the Kinematics of the Compatibility Linkage

1992 ◽  
Author(s):  
J. A. Schaaf ◽  
J. A. Lammers
Keyword(s):  
Complex Number ◽  
Change Point ◽  
Double Point ◽  
Classification Scheme ◽  
Center Point ◽  
Degenerate Form ◽  
Point Curve ◽  
Position Synthesis ◽  
Point Form

Abstract In this paper we develop a method of characterizing the center-point curves for planar four-position synthesis. We predict the five characteristic shapes of the center-point curve using the kinematic classification of the compatibility linkage obtained from a complex number formulation for planar four-position synthesis. This classification scheme is more extensive than the conventional Grashof and non-Grashof classifications in that the separate classes of change point compatibility linkages are also included. A non-Grashof compatibility linkage generates a unicursal form of the center-point curve; a Grashof compatibility linkage generates a bicursal form; a single change point compatibility linkage generates a double point form; and a double or triple change point compatibility linkage generates a circular-degenerate or a hyperbolic-degenerate form.

scholarly journals Spherical Mechanism Synthesis in Virtual Reality

1998 ◽  
Author(s):  
Todd J. Furlong ◽  
Judy M. Vance ◽  
Pierre M. Larochelle
Keyword(s):  
Virtual Reality ◽  
Design Space ◽  
Three Dimensional ◽  
Mechanism Synthesis ◽  
Kinematic Synthesis ◽  
New Approach ◽  
Spherical Mechanisms ◽  
Input Design ◽  
Previous Design ◽  
Spherical Mechanism

Abstract This paper presents a new approach to using virtual reality (VR) to design spherical mechanisms. VR provides a three dimensional design space where a designer can input design positions using a combination of hand gestures and motions and view the resultant mechanism in stereo using natural head movement to change the viewpoint. Because of the three dimensional nature of the design and verification of spherical mechanisms, VR is examined as a new design interface in this research. In addition to providing a VR environment for design, the research presented in this paper has focused on developing a “design in context” approach to spherical mechanism design. Previous design methods have involved placing coordinate frames along the surface of a constraint sphere. The new “design in context” approach allows a designer to freely place geometric models of movable objects inside an environment consisting of fixed objects. The fixed objects could either act as a base for a mechanism or be potential sources of interference with the motion of the mechanism. This approach allows a designer to perform kinematic synthesis of a mechanism while giving consideration to the interaction of that mechanism with its application environment.

Designing Planar Mechanisms Using a Bi-Invariant Metric in the Image Space of SO (3)

1994 ◽  
Author(s):  
Pierre Larochelle ◽  
J. Michael McCarthy
Keyword(s):  
Rigid Body ◽  
Numerical Results ◽  
Image Space ◽  
Dimensional Synthesis ◽  
Invariant Metric ◽  
Planar Mechanisms ◽  
Position And Orientation ◽  
Position Synthesis

Abstract In this paper we present a technique for using a bi-invariant metric in the image space of spherical displacements for designing planar mechanisms for n (> 5) position rigid body guidance. The goal is to perform the dimensional synthesis of the mechanism such that the distance between the position and orientation of the guided body to each of the n goal positions is minimized. Rather than measure these distances in the plane, we introduce an approximating sphere and identify rotations which are equivalent to the planar displacements to a specified tolerance. We then measure distances between the rigid body and the goal positions using a bi-invariant metric on the image space of SO(3). The optimal linkage is obtained by minimizing this distance over all of the n goal positions. The paper proceeds as follows. First, we approximate planar rigid body displacements with spherical displacements and show that the error induced by such an approximation is of order 1/R2, where R is the radius of the approximating sphere. Second, we use a bi-invariant metric in the image space of spherical displacements to synthesize an optimal spherical 4R mechanism. Finally, we identify the planar 4R mechanism associated with the optimal spherical solution. The result is a planar 4R mechanism that has been optimized for n position rigid body guidance using an approximate bi-invariant metric with an error dependent only upon the radius of the approximating sphere. Numerical results for ten position synthesis of a planar 4R mechanism are presented.

Position-Force Synthesis of Closed-Loop Linkages

1994 ◽  
Vol 116 (1) ◽  
pp. 155-162 ◽  
Author(s):  
C. Huang ◽  
B. Roth
Keyword(s):  
Linear Algebra ◽  
Closed Loop ◽  
Screw Theory ◽  
Dimensional Synthesis ◽  
Position Synthesis

The dimensional synthesis of spatial closed-loop linkages to match both force and position specifications is investigated. An efficient means of formulating force equations is introduced through the application of linear algebra to screw theory. The synthesis of spatial four-bar linkages is discussed in detail; it is shown that the maximum number of allowable design positions is not decreased after force constraints are imposed on classical position synthesis problems.

Singularities of Single-DOF Spherical Mechanisms Identified by Means of Pole Axes’ Properties

2010 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Singularity Analysis ◽  
Systems Of Equations ◽  
Planar Mechanisms ◽  
Planar Mechanism ◽  
Geometric Conditions ◽  
Spherical Mechanisms ◽  
Spherical Mechanism ◽  
General Method

Instantaneous pole axes (IPAs) play, in spherical-mechanism kinematics, the same role as instant centers in planar-mechanism kinematics. IPA-based techniques have not been proposed yet for the singularity analysis of spherical mechanisms, even though instant-center-based algorithms have been already presented for planar mechanisms’ singularity analysis. This paper addresses the singularity analysis of single-dof spherical mechanisms by exploiting the properties of pole axes. A general method for implementing this analysis is presented. The presented method relies on the possibility of giving geometric conditions for any type of singularity, and it is the spherical counterpart of an instant-center-based algorithm previously proposed by the author for single-dof planar mechanisms. It can be used to generate systems of equations useful either for finding the singularities of a given mechanism or to synthesize mechanisms that have to match specific requirements about the singularities.

Kinematic Design of a 5-DOF Hybrid Robot with Large Workspace/Limb–Stroke Ratio

2006 ◽  
Vol 129 (5) ◽  
pp. 530-537 ◽  
Author(s):  
Haitao Liu ◽  
Tian Huang ◽  
Jianping Mei ◽  
Xueman Zhao ◽  
Derek G. Chetwynd ◽  
...  
Keyword(s):  
Kinematic Chain ◽  
Open Loop ◽  
Singular Value ◽  
Dimensional Synthesis ◽  
Output Link ◽  
Design Variables ◽  
Spherical Parallel Mechanism ◽  
Symmetry Requirement ◽  
The Mean ◽  
Spherical Mechanism

This paper deals with the conceptual and kinematic designs of a 5-degree of freedom (DOF) reconfigurable hybrid robot. The robot is composed of a 2-DOF parallel spherical mechanism that is serially connected with a 3-DOF open loop kinematic chain via a prismatic joint. Somewhat similar to the well-known Tricept robot, this design has the merit that a relatively large workspace/limb–stroke ratio can be achieved thanks to the decomposition of the motions of the output link into the 2-DOF rotation and 1-DOF translation. As with the Tricept, the robot is well suited for use as a plug-and-play module to configure different machines. The dimensional synthesis of the 2-DOF spherical parallel mechanism is carried out by the monotonical analysis of the design variables versus a global conditioning index represented by the mean of the minimum singular value of the Jacobian, leading to the solution of two nonlinear equations due to the limb length constraint and nearly axial symmetry requirement of the kinematic performance. The results of the dimensional synthesis are given via examples.

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