Geometric Construction of Piecewise Line-Symmetric Spherical Motions Using Quaternion Biarcs

2006 ◽  
Author(s):  
Carlos A. Trujillo ◽  
Q. J. Ge
Keyword(s):  
Gear Train ◽  
Robot Path Planning ◽  
B Spline ◽  
Cam Mechanism ◽  
Epicyclic Gear ◽  
Cad Cam ◽  
Planet Gear ◽  
Velocity Constraints ◽  
C1 Continuity ◽  
Robot Path

This paper employs quaternion biarcs to interpolate a set of orientations with angular velocity constraints. The resulting quaternion curve represents a piecewise spherical line-symmetric rational motion with C1 continuity. Since a quaternion arc corresponds to the motion of the planet gear in a special spherical epicyclic gear train, each segment of the quaternion biarcs can be realized with such an epicyclic gear train. Quaternion biarcs may be used to approximate B-spline quaternion curves that represent rational spherical motions that have applications in robot path planning, CAD/CAM, mechanism design, and computer graphics.

Cycloid Drives With Machining Tolerances

1989 ◽  
Vol 111 (3) ◽  
pp. 337-344 ◽  
Author(s):  
J. G. Blanche ◽  
D. C. H. Yang
Keyword(s):  
High Efficiency ◽  
Dynamic Instability ◽  
Torque Ripple ◽  
Gear Train ◽  
Space Applications ◽  
Input Shaft ◽  
Epicyclic Gear ◽  
Speed Reducer ◽  
Planet Gear ◽  
Gear Mechanism

The cycloidal speed reducer, or cycloid drive, is an epicyclic gear train in which the profile of the planet gear is an epitrochoid and the annular sun gear has rollers as its teeth. The cycloid drive has very high efficiency and small size, in comparison with a conventional gear mechanism, making it an attractive candidate for limited space applications. On the other hand, in this type of transmissions there exist two major drawbacks, namely, backlash and torque ripple. Backlash, the angle through which the output shaft can rotate when the input shaft is held fixed, has a degrading effect on the output accuracy. Torque ripple, the variation in mechanical advantage as the input shaft rotates, causes vibrations and could lead to dynamic instability of the machinery. If the cycloid drive were manufactured to the ideal dimensions, there would be no backlash nor torque ripple. However, in reality, there will always be some machining tolerances. In this paper an analytical model is developed which models the cycloid drive with machining tolerances. Consequently, the effect of machining tolerances on backlash and torque ripple are investigated. It is found that both the backlash and the torque ripple are inherent periodic functions of the input crank angle.

The design of spherical multilobe-cam mechanisms

2009 ◽  
Vol 223 (2) ◽  
pp. 473-482 ◽  
Author(s):  
S Bai ◽  
J Angeles
Keyword(s):  
High Strength ◽  
Gear Train ◽  
Cam Mechanism ◽  
Bevel Gears ◽  
Pressure Angle ◽  
Epicyclic Gear ◽  
Transmission Quality ◽  
Robotic Devices

Cam—roller mechanisms can be used in transmissions and robotic devices as an alternative to their bevel-gear counterparts. As bevel gears are used to couple shafts of intersecting axes, their cam-mechanism replacements are bound to have intersecting axes as well. This means that the contact surface of the cam must be conical, which leads to spherical cam mechanisms. Compared with gear transmissions, cam—roller mechanisms feature low friction, low backlash, and high strength. However, cam mechanisms may end up with a high pressure angle if negative action, a motion in which the cam is driven by mechanism rollers, occurs. This article reports the design of transmissions with spherical multilobe cams (MLCs), as a means to reduce the pressure angle. The kinematics of MLC, including profile generation, undercutting-avoidance, and transmission-quality evaluation, is studied here. A case study has been included, in which the synthesis of a spherical MLC transmission is undertaken as a means to improve the transmission quality of a spherical epicyclic gear train. This train was introduced with the purpose of producing a singularity-free, unlimited-workspace pitch—roll wrist.

scholarly journals Physical-consistent behavior embodied in B-spline curves for robot path planning

2018 ◽  
Vol 51 (22) ◽  
pp. 306-311
Author(s):  
Davide Chiaravalli ◽  
Federico Califano ◽  
Luigi Biagiotti ◽  
Daniele De Gregorio ◽  
Claudio Melchiorri
Keyword(s):  
Path Planning ◽  
Robot Path Planning ◽  
B Spline ◽  
Spline Curves ◽  
Robot Path

scholarly journals Method and Device for Speed Change by the Epicyclic Gear Train with Stepped-Planet Gear Set

2016 ◽  
Vol 38 (1) ◽  
pp. 13-20 ◽  
Author(s):  
Volodymyr Malashchenko ◽  
Oleh Strilets ◽  
Volodymyr Strilets
Keyword(s):  
Change Management ◽  
Gear Train ◽  
Closed Circuit ◽  
Theoretical Research ◽  
Control Element ◽  
Ring Gear ◽  
Variable Speed ◽  
Epicyclic Gear ◽  
Planet Gear ◽  
Speed Change

Abstract The article describes new method and device for continuously variable speed change management via compound epicyclic gearing with composite planet gears and closed circuit hydrosystem, when the speed control element is either outer ring gear (annulus) or the carrier or sun gear. In each case, the control element connected to closed circuit hydrosystem and can be in motion or immovable depending on the bandwidth of hydrosystem’s regulating throttle. We had held theoretical research and received graphic dependences between velocities of driving, control and driven elements by means of computer programing.

Numerical Potential Field Techniques for Robot Path Planning.

1989 ◽  
Author(s):  
Jerome Barraquand ◽  
Bruno Langlois ◽  
Jean-Claude Latombe
Keyword(s):  
Path Planning ◽  
Potential Field ◽  
Robot Path Planning ◽  
Field Techniques ◽  
Robot Path
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