The Synthesis of the Axodes of Spatial Four-Bar Linkages

2012 ◽  
Author(s):  
Giorgio Figliolini ◽  
Pierluigi Rea ◽  
Jorge Angeles
Keyword(s):  
Motion Analysis ◽  
Unit Sphere ◽  
Dual Space ◽  
Moving Frames ◽  
Spatial Motion ◽  
Screw Axis ◽  
Dual Algebra ◽  
Different Types ◽  
Instant Screw Axis ◽  
Four Bar Linkage

The paper introduces a procedure for the motion analysis of a four-bar linkage by means of dual algebra and the Principle of Transference. This procedure allows the mapping of the motion from the Euclidean to the spherical dual space. In particular, the position analysis of a spatial four-bar linkage is formulated by referring to a spherical four-bar linkage, which moves on the dual unit sphere. Moreover, both fixed and moving axodes of the coupler link are obtained, as traced by the spatial motion of the instant screw axis (ISA) with respect to the fixed and moving frames. These ruled surfaces reproduce the spatial motion of the coupler link upon relatively rolling and sliding around and along the ISA. Finally, the proposed procedure has been implemented in MatLab, in order to analyze the motion of the different types of four-bar linkages, including the Bennett mechanism and the Hooke joint. The motion is illustrated by means of animations of the four-bar linkages and their axodes.

The Synthesis of the Pitch Surfaces of Internal and External Skew-Gears and Their Racks

2005 ◽  
Vol 128 (4) ◽  
pp. 794-802 ◽  
Author(s):  
Giorgio Figliolini ◽  
Jorge Angeles
Keyword(s):  
Euclidean Space ◽  
Dual Space ◽  
Spatial Motion ◽  
Screw Axis ◽  
Dual Algebra ◽  
Screw Motion ◽  
Bevel Gears ◽  
The Subject ◽  
Instant Screw Axis ◽  
Spherical Motion

The synthesis of the pitch surfaces of any pair of external and internal skew gears, using dual algebra and the principle of transference, is the subject of this paper. The spatial motion of the Euclidean space is transferred to the dual space in order to obtain a simplified dual spherical motion, thus emulating the motion of bevel gears. The relative screw motion is hence analyzed by determining the position of the instant screw axis and the angular and sliding velocities. Moreover, the hyperboloid pitch surfaces of the driving and driven gears are synthesized, along with the helicoid pitch surface of their rack. Several numerical results are reported.

The Synthesis of the Axodes of RCCC Linkages

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Giorgio Figliolini ◽  
Pierluigi Rea ◽  
Jorge Angeles
Keyword(s):  
Ruled Surface ◽  
Line Contact ◽  
Output Function ◽  
Input Output ◽  
Screw Axis ◽  
Dual Algebra ◽  
Synthesis Procedure ◽  
Instant Screw Axis ◽  
Four Bar Linkage

As the coupler link of an RCCC linkage moves, its instant screw axis (ISA) sweeps a ruled surface on the fixed link; by the same token, the ISA describes on the coupler link itself a corresponding ruled surface. These two surfaces are the axodes of the linkage, which roll while sliding and maintaining line contact. The axodes not only help to visualize the motion undergone by the coupler link but also can be machined as spatial cams and replace the four-bar linkage, if the need arises. Reported in this paper is a procedure that allows the synthesis of the axodes of an RCCC linkage. The synthesis of this linkage, in turn, is based on dual algebra and the principle of transference, as applied to a spherical four-bar linkage with the same input–output function as the angular variables of the RCCC linkage. Examples of RCCC linkages are included. Moreover, to illustrate the generality of the synthesis procedure, it is also applied to a spherical linkage, namely, the Hooke joint, and to the Bennett linkage.

Generation of Noncircular Bevel Gears With Free-Form Tooth Profile and Curvilinear Tooth Lengthwise

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Fangyan Zheng ◽  
Lin Hua ◽  
Xinghui Han ◽  
Dingfang Chen
Keyword(s):  
Screw Theory ◽  
Mapping Method ◽  
Tooth Profile ◽  
Bevel Gear ◽  
Free Form ◽  
Arc Length ◽  
Screw Axis ◽  
Bevel Gears ◽  
Generating Method ◽  
Instant Screw Axis

Noncircular bevel gear is applied to intersecting axes, realizing given function of transmission ratio. Currently, researches are focused mainly on gear with involute tooth profile and straight tooth lengthwise, while that with free-form tooth profile and curvilinear tooth lengthwise are seldom touched upon. Based on screw theory and equal arc-length mapping method, this paper proposes a generally applicable generating method for noncircular bevel gear with free-form tooth profile and curvilinear tooth lengthwise, covering instant screw axis, conjugate pitch surface, as well as the generator with free-form tooth profile and curvilinear tooth lengthwise. Further, the correctness of the proposed method is verified through illustrations of computerized design.

A Generalized Kinematic for Calculating and Evaluating Surface Geometry of Gears and Cutting Tools

1992 ◽  
Author(s):  
J. Grill ◽  
K. H. Hirschmann ◽  
G. Lechner
Keyword(s):  
General Equation ◽  
Cutting Tools ◽  
Grinding Process ◽  
Spatial Motion ◽  
Line Geometry ◽  
Surface Geometry ◽  
Screw Axis ◽  
On Line ◽  
Instantaneous Screw Axis ◽  
Instantaneous Screw

Abstract A new method for simulating the cutting and grinding process of gears has been developed. The procedure, implemented on a workstation, allows to describe the most general case of spatial motion based on line coordinates. The meshing of two gears is replaced by the motion of two axodes, rolling and sliding on each other about and along the instantaneous screw axis. A general equation of meshing has been developed, also based on line geometry. Velocity, acceleration and jerk can be determined, which are used for calculating the generated surfaces and their derivatives.

scholarly journals The integration of CAD and motion analysis into a single intuitive software package

2002 ◽  
Author(s):  
◽  
Nitin J. Daya
Keyword(s):  
Motion Analysis ◽  
Software Package ◽  
General Purpose ◽  
Complex Activity ◽  
Cad Systems ◽  
Cad System ◽  
Different Types

Existing CAD systems cannot satisfy all the requirements of 'real' design. Many designers would like to have more powerful and capable CAD systems. 'Real' design is a complex activity involving different types of problems thus a CAD system must be a general purpose system so that it can support all aspects of design including that of motion analysis.

Acceleration Analysis of Spatial Linkages Using Axodes and the Instantaneous Screw Axis

1967 ◽  
Vol 89 (1) ◽  
pp. 97-101 ◽  
Author(s):  
M. Skreiner
Keyword(s):  
Rigid Bodies ◽  
General Point ◽  
Spatial Motion ◽  
Input Output ◽  
Screw Axis ◽  
Acceleration Analysis ◽  
Instantaneous Screw Axis ◽  
Spatial Linkages ◽  
Output Information ◽  
Instantaneous Screw

The application of recent techniques developed in the geometry and the kinematics of instantaneous spatial motion generated by a pair of axodes, and the relative spatial motion of three rigid bodies using the instantaneous screw axis is demonstrated in an analysis of the Bennett Mechanism. Explicit equations which are well suited to machine calculations yield input-output information, the location and the properties of the instantaneous screw axis, the characteristic properties of the axodes, the velocity and the acceleration of a general point in the moving link, and the position of the center of acceleration in the moving link.

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