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# Kinematic Analysis of Planetary Gear Systems Using Block Diagrams

[+] Author and Article Information
Mi-Ching Tsai

Department of Mechanical Engineering, National Cheng Kung University, Tainan 70101, Taiwanmctsai@mail.ncku.edu.tw

Cheng-Chi Huang

Department of Mechanical Engineering, National Cheng Kung University, Tainan 70101, Taiwann1895146@mail.ncku.edu.tw

Bor-Jeng Lin

Department of Automation Engineering, National Formosa University, Yunlin 63201, Taiwanbjlin@nfu.edu.tw

J. Mech. Des 132(6), 065001 (May 25, 2010) (10 pages) doi:10.1115/1.4001598 History: Received August 03, 2009; Revised March 29, 2010; Published May 25, 2010; Online May 25, 2010

## Abstract

This paper employs control techniques to analyze kinematic relationships via block diagrams for planetary gear systems. The revealed tangent-velocity equations at each contact point of the mechanical gearsets are utilized to plot the block diagrams. Then, the concepts of feedback and feedforward strategies are adopted to illustrate speed-reduction and increasing functions in kinematics with sensitivity analysis. The structural difference between unusual planetary gears and common ones is also explained based on the characteristic equation of feedback strategies for structural constraints in terms of stability conditions. A cam-controlled planetary gear is further illustrated for the constraint and kinematic analysis by using the block diagram technique and characteristic equation, and the computational simulations for the sensitivity and the motion output of this planetary gear are obtained. Through the correspondence between control and kinematics, this paper provides a guide for engineers in various fields to easily understand the function of mechanical design.

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## Figures

Figure 1

Block diagrams of common control systems: (a) forward system (open-loop) and (b) feedback system (closed-loop)

Figure 3

Basic epicyclic gearset: (a) velocity diagram and (b) basic modeling (ωc is output)

Figure 4

Velocity diagram of planetary gearbox

Figure 5

Model of Mode 1

Figure 6

Models of (a) Mode 2 and (b) Mode 3

Figure 11

Simulation of Mode A of cam-controlled planetary gear: (a) cam profile, (b) ωSR, and (c) ωSR(1/Z)

Figure 12

Simulation of Mode A of cam-controlled planetary gear: (a) ωc(1/Z−1) and (b) angular velocity of sun gear ωs

Figure 13

Conditions and simulations of Mode B of cam-controlled planetary gear: (a) 1/Z(1−dθr/dθc), (b) 1/Z, and (c) angular velocity of carrier ωc

Figure 14

Gain sensitivities for Mode B of cam-controlled planetary gear: (a) 1/Z−1 and (b) 1/Z and dθr/dθc

Figure 7

Planetary differential gear (1)

Figure 10

Sketch and models of cam-controlled planetary gear: (a) sketch, (b) Mode A, and (c) Mode B

Figure 2

Block diagrams of common control systems with the second input D: (a) feedback system and (b) feedforward system

Figure 8

Model of planetary differential gear

Figure 9

Compound planetary gear drive: (a) sketches and (b) model

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