Epicyclic Gear Trains: Analysis, Synthesis and Applications

Müller, H.; Willis, Robert J.

doi:10.1115/1.3267356

Cited by 17 publications

(31 citation statements)

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“…The advantages of planetary gears over parallel axis gears include high power density, large gear reduction in a small volume, multiple kinematic combinations, pure torsional reactions and coaxial shafting. Among the disadvantages one can note high bearing loads, inaccessibility and design complexity [15]. According to [15] and [16] Willis relation for planetary mechanical gear is given by (1) where is the angular velocity of the sun gear, is the angular velocity of ring gear, is the angular velocity of the planet carrier, and is basic train gear ratio.…”

Section: A Principle Of Operationmentioning

confidence: 99%

“…Among the disadvantages one can note high bearing loads, inaccessibility and design complexity [15]. According to [15] and [16] Willis relation for planetary mechanical gear is given by (1) where is the angular velocity of the sun gear, is the angular velocity of ring gear, is the angular velocity of the planet carrier, and is basic train gear ratio. The value of basic train gear ratio for single stage planetary gear is calculated using (2) (2) where and are respectively the number of teeth of the sun gear and the ring gear.…”

Section: A Principle Of Operationmentioning

confidence: 99%

“…3, the components of the forces at the contact point , Fig. 4, are (13) (14) (15) where are respectively the normal, the tangential and the radial forces exerted by gear one on gear two. Reciprocally, the principle of action-reaction leads to the same forces (exerted by gear two on gear one) as in (13), (14), and (15).…”

Section: Planetary Gear Forces and Stressmentioning

confidence: 99%

“…In determining the values of and , the gears are regarded as ideal. The determination of each (22) factor in the bending strength equation is described in detail in [15], [17]- [20] ( 22) Notice that the gear face width should be selected in the range (9 m-15 m). In this paper, a value m is chosen.…”

Section: ) Bending Strength Of Spur Gearsmentioning

confidence: 99%

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Comparative Study Between Mechanical and Magnetic Planetary Gears

et al. 2011

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The paper deals with the possibility of replacing a mechanical planetary gear system by a magnetic planetary gearbox. The magnetic planetary gearbox has many advantages such as contact-free, no gear lubrication, high-speed-reduction ratio and high durability. Firstly, the principle of operation, design equations and Willis relation for the magnetic and the mechanical planetary gears are given. A comparative study between the two systems in terms of torque transmission capabilities is presented.Index Terms-Gearbox, high torque density, magnetic planetary gears, mechanical planetary gears, Willis equation. NOMENCLATURERelated to sun, planet, ring, and planet carrier gears respectively (mechanical gear).Related to inner rotor, steel pole pieces, outer rotor, and carrier steel pole pieces respectively (magnetic gear). Rotational velocity of the inner rotor and the sun gear.Rotational velocity of the planet gear.Rotational velocity of the outer rotor and the ring gear.Rotational velocity of the carrier steel pole pieces and the planet carrier.Basic train gear ratio.Number of teeth of the sun, the planet and the ring.Diameter of the sun, the planet and the ring.Outer diameter of the ring gear.Pitch circle diameter, base circle diameter.Input torque at the sun gear or at the inner rotor.Output torque at the ring gear or at the outer rotor.Torque at gear one (the sun gear).Gear ratio.Tangential force.Tangential force exerted by the planet on the sun teeth.

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Section: A Principle Of Operationmentioning

confidence: 99%

Section: A Principle Of Operationmentioning

confidence: 99%

Section: Planetary Gear Forces and Stressmentioning

confidence: 99%

Section: ) Bending Strength Of Spur Gearsmentioning

confidence: 99%

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Comparative Study Between Mechanical and Magnetic Planetary Gears

et al. 2011

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“…The positive-ratio planetary gear train includes a first sun gear ps1 mounted on the rotational shaft pss1, a second sun gear ps2 mounted on the rotational shaft pss2, at least one compound planet gear set that includes gears pp1 and pp2 and meshes with the first and the second sun gears, and a planet gear carrier pa. A positive-ratio planetary gear train means that the shafts of the first and second sun gears, when the carrier is fixed, have the same direction of rotation. Therefore, its basic speed-ratio, which is defined as the ratio of the relative shaft velocities of the first and the second sun gears with respect to the carrier, is consequently positive and cannot be equal to 1 [13]. The shafts of the first sun gear, the second sun gear, and the carrier are the rotational shafts of each planetary gear train in the ICT mechanism, namely AD, OP, and AE, or BD, CR, and BE, as shown in Figure 2, (4) where N is the number of teeth on the gear indicated by its subscript.…”

Section: Positive-ratio Planetary Gear Trainmentioning

confidence: 99%

Kinematic Analyses of a Parallel-type Independently Controllable Transmission

Hwang

Tsay

Liao

et al. 2011

AUSMT

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This study proposes a novel design of a parallel-type Independently Controllable Transmission (ICT). The parallel-type ICT can produce a continuously variable transmission ratio and a required angular output velocity that can be independently manipulated by a controller yet not affected by the angular velocity of the input shaft. The proposed parallel-type ICT is composed of two planetary gear trains and two transmission-connecting members. A prototype was built to investigate its kinematic characteristics and verify application feasibility

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Scaling laws for robotic transmissions

Saerens

Crispel

García

et al. 2019

Mechanism and Machine Theory

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In robotic actuators, low speeds and high torques are usually required. Small electric motors, which are more efficient at high speeds and low torques, do not fit the requirements directly. In order to transform the motor characteristics into the desired output characteristics, a transmission system is needed. Ideally, it should be optimally designed and adapted to the desired characteristics and the available space. Scaling laws can provide a way to design these desired output requirements as a function of the size parameters. These are however not yet available for transmission systems. To fill this gap, several scaling laws are developed throughout this paper for some of the most important robotic characteristics, i.e. maximum continuous output torque and reflected inertia, in function of the number of stages, the transmission ratio and the size parameters of different types of transmissions. These laws show that diameter has a much bigger influence on the characteristics of transmissions than length. All derived laws show good comparison with catalog data of manufacturers like Maxon, Moog, Neugart, Harmonic Drive , Sumitomo and SKF.

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Epicyclic Gear Trains: Analysis, Synthesis and Applications

Cited by 17 publications

References 0 publications

Comparative Study Between Mechanical and Magnetic Planetary Gears

Comparative Study Between Mechanical and Magnetic Planetary Gears

Kinematic Analyses of a Parallel-type Independently Controllable Transmission

Scaling laws for robotic transmissions

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