Mobility and Geometric Analysis of the Hoberman Switch-Pitch Ball and Its Variant

2010 ◽  
Vol 2 (3) ◽  
Author(s):  
Guowu Wei ◽  
Xilun Ding ◽  
Jian S. Dai
Keyword(s):  
Geometric Analysis ◽  
Loop Equation ◽  
Bevel Gears ◽  
Kinematic Characteristics ◽  
Special Case ◽  
Geometry And Kinematics

This paper investigates the mobility and kinematics of the Hoberman switch-pitch ball, and particularly, its variant that does not resort to bevel gears. The ball variant is a general case of the Hoberman switch-pitch ball and constitutes the ball. This paper starts from examining the geometry of the ball variant and its composition, and decomposes it into loops containing eight-bar radially foldable linkages. To investigate the eight-bar radially foldable linkage, constraint matrices are developed using the screw-loop equation. This paper extends the study to the ball variant and investigates the singularity and various configurations based on the geometry and kinematics of the ball variant. This leads to the investigation of the Hoberman switch-pitch ball as a special case of the ball variant with bevel gears to simultaneously drive three joints in every vertex of the ball mechanism. The analysis is then followed by a numerical demonstration of the kinematic characteristics of the Hoberman switch-pitch ball.

Geometric and Kinematic Analysis of the Hoberman Switch-Pitch Ball and Its Variant

2009 ◽  
Author(s):  
Guowu Wei ◽  
Xilun Ding ◽  
Jian S. Dai
Keyword(s):  
Kinematic Analysis ◽  
Numerical Example ◽  
Bevel Gears ◽  
Kinematic Characteristics ◽  
Special Case ◽  
Geometry And Kinematics

This paper investigates geometry and kinematics of the Hoberman switch-pitch ball and its variant as an extended case of the ball. The paper starts from examining the geometry of the ball variant and its composition and decomposes it into loops each of which is an eight-bar radial linkage. Based on this, the paper investigates the geometry of the eight-bar radial linkage and the variant and subsequently extends the study to their kinematics. The Hoberman switch-pitch ball as a special case of the ball variant with bevel gears is investigated and a numerical example is employed to illustrate the kinematic characteristics of the eight-bar radial linkage and the Hoberman switch-pitch ball.

Linkages That Transfer Rotations to Radially Reciprocating Motion

2010 ◽  
Author(s):  
Guowu Wei ◽  
Jian S. Dai
Keyword(s):  
Constraint Equation ◽  
Equation Method ◽  
Reciprocating Motion ◽  
Loop Equation ◽  
Revolute Joints ◽  
Kinematic Characteristics ◽  
Overconstrained Linkages ◽  
Geometry And Kinematics

Stemming from study of polyhedral and spheroidal linkages and investigation of reciprocating motion of the PRRP chain, this paper presents four overconstrained linkages that are capable of transferring rotations to radially reciprocating motion. The linkages connected by revolute joints are of symmetrical arrangement and mobility one and are analysed by using the screw-loop equation method. The paper further investigates geometry and kinematics of the linkages and reveals their kinematic characteristics, leading to the constraint equation.

Kinematic Investigation of the Deployable Bennett Loop

2006 ◽  
Vol 129 (6) ◽  
pp. 602-610 ◽  
Author(s):  
J. Eddie Baker
Keyword(s):  
Full Advantage ◽  
Spatial Displacement ◽  
Learning Tool ◽  
Working Mechanism ◽  
Efficient Treatment ◽  
Kinematic Characteristics ◽  
The Subject ◽  
The Many ◽  
Special Case

Despite the many studies devoted to it and its value as a learning tool, the Bennett linkage has never been employed as a working mechanism. It has recently found favor, however, among structural analysts as a possible unit in deployable networks owing to the potential for true spatial displacement without flexure. Although the loop can be analyzed in this application by means of purely geometrical methods, a wealth of kinematic examinations is available for more efficient treatment. The particular form that the chain must adopt as a deployable object and the special case of the linkage demanded by the purpose constitute the subject of the present exposition, which takes full advantage of prior analyses of the chain’s kinematic characteristics.

Synthesis, Mobility, and Multifurcation of Deployable Polyhedral Mechanisms With Radially Reciprocating Motion

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
Guowu Wei ◽  
Yao Chen ◽  
Jian S. Dai
Keyword(s):  
Geometric Constraints ◽  
Reciprocating Motion ◽  
Single Plane ◽  
Plane Symmetric ◽  
Loop Equation ◽  
Dual Plane ◽  
Potential Applications ◽  
Number Synthesis ◽  
First Time ◽  
Geometry And Kinematics

Extending the method coined virtual-center-based (VCB) for synthesizing a group of deployable platonic mechanisms with radially reciprocating motion by implanting dual-plane-symmetric 8-bar linkages into the platonic polyhedron bases, this paper proposes for the first time a more general single-plane-symmetric 8-bar linkage and applies it together with the dual-plane-symmetric 8-bar linkage to the synthesis of a family of one-degree of freedom (DOF) highly overconstrained deployable polyhedral mechanisms (DPMs) with radially reciprocating motion. The two 8-bar linkages are compared, and geometry and kinematics of the single-plane-symmetric 8-bar linkage are investigated providing geometric constraints for synthesizing the DPMs. Based on synthesis of the regular DPMs, synthesis of semiregular and Johnson DPMs is implemented, which is illustrated by the synthesis and construction of a deployable rectangular prismatic mechanism and a truncated icosahedral (C60) mechanism. Geometric parameters and number synthesis of typical semiregular and Johnson DPMs based on the Archimedean polyhedrons, prisms and Johnson polyhedrons are presented. Further, movability of the mechanisms is evaluated using symmetry-extended rule, and mobility of the mechanisms is verified with screw-loop equation method; in addition, degree of overconstraint of the mechanisms is investigated by combining the Euler's formula for polyhedrons and the Grübler–Kutzbach formula for mobility analysis of linkages. Ultimately, singular configurations of the mechanisms are revealed and multifurcation of the DPMs is identified. The paper hence presents an intuitive and efficient approach for synthesizing PDMs that have great potential applications in the fields of architecture, manufacturing, robotics, space exploration, and molecule research.

Topology of Spade Drills for Wood Drilling Operations, Part 1: Spade Drill Point Geometry Definition

2005 ◽  
Vol 127 (2) ◽  
pp. 298-309
Author(s):  
Hanxin Zhao ◽  
Kornel F. Ehmann
Keyword(s):  
Mathematical Model ◽  
Construction Industry ◽  
Software Package ◽  
Geometric Analysis ◽  
Analytical Models ◽  
Basic Design ◽  
Technical Literature ◽  
Drilling Operations ◽  
Drill Point ◽  
Geometry And Kinematics

Spade bits, widely and routinely used in the construction industry, have not received any attention in the technical literature, yet there is a pressing need to improve the performance of these bits whose basic design has not changed for decades. To facilitate such improvements, a thorough understanding of the geometric, manufacturing, and cutting mechanics aspects of these tools is necessary. In this two-part paper, the point geometry and manufacturing issues will be discussed. To fundamentally understand the spade drill bit’s behavior, a complete mathematical model of its principal topological elements will be established. In conjunction with this model, the corresponding analytical formulations of the geometry and kinematics of the appropriate manufacturing procedures will also be formulated. In unison, these models will lay the foundation for a methodology and a software package for a detailed geometric analysis of all relevant cutting angle distributions and edge profiles of the spade bit. This will facilitate, at a later point, new point developments rooted in rigorous analytical models.

scholarly journals A New 6 DOF Robotic Arm with Linkage Motion Mechanism and Actuators Placed in Base

2016 ◽  
Vol 5 (1) ◽  
pp. 35
Author(s):  
Mohsen Shahhosseini ◽  
Rambod Rastegari ◽  
Roozbeh Abbasi
Keyword(s):  
Mechanism Design ◽  
Degrees Of Freedom ◽  
Robotic Arm ◽  
Linkage Mechanism ◽  
Performance Simulation ◽  
Motion Mechanism ◽  
Six Degrees Of Freedom ◽  
Bevel Gears ◽  
Controller Performance ◽  
Special Case

<p>We examined mechanism design and kinematic simulation of a new six degrees of freedom (DOF) robotic arm with rotational joints and a linkage motion mechanism. In the design, a parallel linkage mechanism, accompanied by an additional set of bevel gears, was used to create the desired motion for all six links along with transfer of all actuators to the robot’s base to reduce the mass of most of the arms. These changes resulted in reduction of the torque required for joints 1, 2, and 3. Using this parallel mechanism ensures dependence to motion links and creates a special case for the control of the robot and more rigidity against unwanted movement. Initially, we examined mechanism design methods for a parallel linkage mechanism and considered methods for application in an operational robot. In the next step, we determined the kinematic relationships that were established between the robot’s actuators and joints spaces due to the use of this mechanism. Then, we developed an example of the robot’s function in a performance simulation. The simulation results indicated that the mechanism and controller performance were acceptable.</p>

Geometry and Kinematics of a Plane-Symmetric Spatial Eight-Bar Linkage With Exact Straight-Line Motion

2011 ◽  
Author(s):  
Guowu Wei ◽  
Jian S. Dai
Keyword(s):  
Isosceles Triangle ◽  
Plane Symmetric ◽  
Straight Line ◽  
Translation Motion ◽  
Motion Characteristics ◽  
First Time ◽  
The Relationship ◽  
Special Case ◽  
Kinematic Properties ◽  
Geometry And Kinematics

In this paper, a novel plane-symmetric spatial eight-bar linkage with exact straight-line motion is proposed for the first time. Geometry and kinematics of the eight-bar linkage are studied and closed-form equations are presented revealing the exact straight-line motion characteristics of the linkage. It is found in this paper that, for the plane-symmetric eight-bar linkage, the angle α between the base and the straight-line traced by the trajectory of the end-effector point is only dependent on the angle φ of the isosceles triangle vertexes of the linkage but independent of the length of the links and dimension of the vertexes. The relationship between α and φ is studied and a special case that leads to parallel translation motion is revealed. Numerical example is then given to illustrate the kinematic properties of the eight-bar linkage.

A Geometric-Algebraic Exploration of Two Kinds of Schatz 6R Linkages

1998 ◽  
Author(s):  
Chung-Ching Lee
Keyword(s):  
Geometric Analysis ◽  
Algebraic Surfaces ◽  
View Point ◽  
Constrained Motion ◽  
Screw Axis ◽  
Loop Equation ◽  
Closed Form Solutions ◽  
Single Screw ◽  
The Matrix ◽  
Matrix Differential

Abstract The generation of two kinds of Schatz six-revolute linkages is first delineated from the view point of geometry and then, the general analytical kinematic closed-form solutions of both types are developed by matrix algebra and its differentiation for confirming the constrained motion and further application. The full cycle range of motion about the input link for these linkages is also verified by using the matrix differential closure loop equation. Furthermore, based on the six-by-six screw coordinate transformation matrix, we establish the algebraic formulas of screw coordinates of six-revolute joint axes and the single screw axis reciprocal to the five-order screw system defined by the joint axes of linkages. Then we make their algebraic and geometric analysis with the help of 3D computer graphics. Two kinds of algebraic surfaces for both linkages’ reciprocal screws are presented for understanding the real features and for proving the fact that during their cycles of movement there are no transversal to all six-revolue joint axes permanently.

Extreme self-sacrifice beyond fusion: Moral expansiveness and the special case of allyship

2018 ◽  
Vol 41 ◽  
Author(s):  
Daniel Crimston ◽  
Matthew J. Hornsey
Keyword(s):  
General Theory ◽  
Biological Markers ◽  
Natural Environment ◽  
Relevant Dimension ◽  
Special Case

AbstractAs a general theory of extreme self-sacrifice, Whitehouse's article misses one relevant dimension: people's willingness to fight and die in support of entities not bound by biological markers or ancestral kinship (allyship). We discuss research on moral expansiveness, which highlights individuals’ capacity to self-sacrifice for targets that lie outside traditional in-group markers, including racial out-groups, animals, and the natural environment.

Determination of the phase structure of polymerblends by electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 492-493
Author(s):  
Dr. G. Kaemof
Keyword(s):  
Screw Extruder ◽  
Electron Microscopic ◽  
Thin Sections ◽  
Single Screw Extruder ◽  
Transmission Electron ◽  
The Matrix ◽  
Twin Screw ◽  
Special Case ◽  
Microscopic Investigations

A mixture of polycarbonate (PC) and styrene-acrylonitrile-copolymer (SAN) represents a very good example for the efficiency of electron microscopic investigations concerning the determination of optimum production procedures for high grade product properties.The following parameters have been varied:components of charge (PC : SAN 50 : 50, 60 : 40, 70 : 30), kind of compounding machine (single screw extruder, twin screw extruder, discontinuous kneader), mass-temperature (lowest and highest possible temperature).The transmission electron microscopic investigations (TEM) were carried out on ultra thin sections, the PC-phase of which was selectively etched by triethylamine.The phase transition (matrix to disperse phase) does not occur - as might be expected - at a PC to SAN ratio of 50 : 50, but at a ratio of 65 : 35. Our results show that the matrix is preferably formed by the components with the lower melting viscosity (in this special case SAN), even at concentrations of less than 50 %.

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