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.

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 Role of the Orthogonal Helicoid in the Generation of the Tooth Flanks of Involute-Gear Pairs With Skew Axes

2014 ◽  
Author(s):  
Giorgio Figliolini ◽  
Hellmuth Stachel ◽  
Jorge Angeles
Keyword(s):  
Tangent Plane ◽  
Line Contact ◽  
Screw Axis ◽  
Fundamental Step ◽  
Involute Gear ◽  
Involute Gears ◽  
Instant Screw Axis

Camus’ concept of Auxiliary Surface (AS) is extended to the case of involute gears with skew axes. In the case at hand, we show that the AS is an orthogonal helicoid whose axis a) lies in the cylindroid and b) is normal to the instant screw axis of one gear with respect to its meshing counterpart; in general, the helicoid axis is skew with respect to the latter. According to the spatial version of Camus’ Theorem, any line attached to the AS, in particular any generator g of AS itself, can be chosen to generate a pair of conjugate flanks with line contact. While the pair of conjugate flanks is geometrically feasible, as they always share a line of contact and the tangent plane at each point of this line, there are poses where the flanks even have a common Disteli axis. Then there is a G2-contact at the striction point and the two surfaces penetrate each other. The outcome is that the surfaces are not realizable as tooth flanks. Nevertheless, this is a fundamental step towards the synthesis of the flanks of involute gears with skew axes.

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 Role of the Orthogonal Helicoid in the Generation of the Tooth Flanks of Involute-Gear Pairs With Skew Axes

2015 ◽  
Vol 7 (1) ◽  
Author(s):  
Giorgio Figliolini ◽  
Hellmuth Stachel ◽  
Jorge Angeles
Keyword(s):  
Smooth Surface ◽  
Tangent Plane ◽  
Line Contact ◽  
Planar Surface ◽  
Screw Axis ◽  
Bevel Gears ◽  
Involute Gears ◽  
G2 Continuity ◽  
Instant Screw Axis

Camus' concept of auxiliary surface (AS) is extended to the case of involute gears with skew axes. In the case at hand, we show that the AS is an orthogonal helicoid whose axis (a) lies in the cylindroid and (b) is normal to the instant screw axis of one gear with respect to its meshing counterpart; in general, the helicoid axis is skew with respect to the latter. According to the spatial version of Camus' Theorem, any line or surface attached to the AS, in particular any line L of AS itself, can be chosen to generate a pair of conjugate flanks with line contact. While the pair of conjugate flanks is geometrically feasible, as they always share a line of contact and the tangent plane at each point of this line, they even have the same curvature, G2-continuity, when L coincides with the instant screw axis (ISA). This means that the two surfaces penetrate each other, at the same common line. The outcome is that the surfaces are not realizable as tooth flanks. Nevertheless, this is a fundamental step toward the synthesis of the flanks of involute gears with skew axes. In fact, the above-mentioned interpenetration between the tooth flanks can be avoided by choosing a smooth surface attached to the AS, instead of a line of the AS itself, which can give, in particular, the spatial version of octoidal bevel gears, when a planar surface is chosen.

scholarly journals Identification of Brain Electrical Activity Related to Head Yaw Rotations

Sensors ◽  
2021 ◽  
Vol 21 (10) ◽  
pp. 3345
Author(s):  
Enrico Zero ◽  
Chiara Bersani ◽  
Roberto Sacile
Keyword(s):  
Electrical Activity ◽  
Electrical Stimulus ◽  
Head Movements ◽  
Brain Electrical Activity ◽  
Output Function ◽  
Input Output ◽  
Eeg Signals ◽  
Head Turning ◽  
Identification Technique ◽  
The Brain

Automatizing the identification of human brain stimuli during head movements could lead towards a significant step forward for human computer interaction (HCI), with important applications for severely impaired people and for robotics. In this paper, a neural network-based identification technique is presented to recognize, by EEG signals, the participant’s head yaw rotations when they are subjected to visual stimulus. The goal is to identify an input-output function between the brain electrical activity and the head movement triggered by switching on/off a light on the participant’s left/right hand side. This identification process is based on “Levenberg–Marquardt” backpropagation algorithm. The results obtained on ten participants, spanning more than two hours of experiments, show the ability of the proposed approach in identifying the brain electrical stimulus associate with head turning. A first analysis is computed to the EEG signals associated to each experiment for each participant. The accuracy of prediction is demonstrated by a significant correlation between training and test trials of the same file, which, in the best case, reaches value r = 0.98 with MSE = 0.02. In a second analysis, the input output function trained on the EEG signals of one participant is tested on the EEG signals by other participants. In this case, the low correlation coefficient values demonstrated that the classifier performances decreases when it is trained and tested on different subjects.

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.

SIXPAQ: A Comprehensive Software Package for Analysis and Synthesis of Six-Bar Dwell Linkages

1991 ◽  
Author(s):  
Max Antonio González-Palacios ◽  
Jorge Angeles
Keyword(s):  
Software Package ◽  
Input Output ◽  
Robust Algorithms ◽  
Interactive Analysis ◽  
Analysis And Synthesis ◽  
Synthesis Procedure ◽  
Linkage Synthesis

Abstract SIXPAQ is a software package that was created for the interactive analysis and synthesis of six-bar dwell linkages. The package is structured so that any six-bar dwell planar linkage can be designed by simply choosing a reduced number of parameters. Robust algorithms are introduced that allow an accurate and reliable construction of the two loci on which the linkage synthesis procedure is based. Input-output plots and animation are available within the package as visualization aids. The package allows the user to interact with the program to satisfy the dwell and geometry conditions. Animation is achieved using a powerful graphics workstation.

Computer simulation of the steady-state input-output function of the cat medial gastrocnemius motoneuron pool

1991 ◽  
Vol 65 (4) ◽  
pp. 952-967 ◽  
Author(s):  
C. J. Heckman ◽  
M. D. Binder
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Motor Unit ◽  
Frequency Modulation ◽  
Motor Units ◽  
Medial Gastrocnemius ◽  
Output Function ◽  
Input Output ◽  
Motoneuron Pool ◽  
Random Variance

1. A pool of 100 simulated motor units was constructed in which the steady-state neural and mechanical properties of the units were very closely matched to the available experimental data for the cat medial gastrocnemius motoneuron pool and muscle. The resulting neural network generated quantitative predictions of whole system input-output functions based on the single unit data. The results of the simulations were compared with experimental data on normal motor system behavior in humans and animals. 2. We considered only steady-state, isometric conditions. All motoneurons received equal proportions of the synaptic input, and no feedback loops were operative. Thus the intrinsic properties of the motor unit population alone determined the form of the system input-output function. Expressing the synaptic input in terms of effective synaptic current allowed the simulated motoneuron input-output functions to be specified by well-known firing rate-injected current relations. The motor unit forces were determined from standard motor unit force-frequency relations, and the system output at any input level was assumed to be the linear sum of the forces of the active motor units. 3. The steady-state input-output function of the simulated motoneuron pool had a roughly sigmoidal shape that was quite different from those derived from previous recruitment models, which did not incorporate frequency modulation. Frequency modulation in combination with the skewed distribution of thresholds (low values much more frequent than high) restricted upward curvature to low input levels, whereas frequency modulation alone was responsible for the final gradual approach to the maximum force output. 4. Sensitivity analyses were performed to assess the importance of several assumptions that were required to deal with gaps and uncertainties in the available experimental data. The shape of the input-output function was not critically dependent on any of these assumptions, including those specifying linear summation of inputs and outputs. 5. A key assumption of the model was that systematic variance in motor unit properties was much more important than random variance for determining the input-output function. Addition of random variance via Monte Carlo techniques showed that this assumption was correct. These results suggest that the output of a motoneuron pool should be quite tolerant of random variance in the distribution of synaptic inputs and yet substantially altered by any systematic differences, such as unequal distribution of inputs among different motor unit types.(ABSTRACT TRUNCATED AT 400 WORDS)

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