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Research Papers: Design of Mechanisms and Robotic Systems

Parametric Design of Scalable Mechanisms for Additive Manufacturing

[+] Author and Article Information
Xianda Li

Institute of Intelligent Manufacturing and
Information Engineering,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: sbnine@sjtu.edu.cn

Jie Zhao

Department of Physics and Astronomy,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: carrotzhao@sjtu.edu.cn

Ren He

Institute of Intelligent Manufacturing and
Information Engineering,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: hrmuye@sjtu.edu.cn

Yaobin Tian

Department of Industrial Engineering
and Logistics Management,
Hong Kong University of Science
and Technology,
Clear Water Bay,
Kowloon, Hong Kong
e-mail: ybtian@ust.hk

Xiangzhi Wei

Institute of Intelligent Manufacturing and
Information Engineering,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China e-mail: antonwei@sjtu.edu.cn

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received May 17, 2017; final manuscript received October 7, 2017; published online December 11, 2017. Assoc. Editor: Ettore Pennestri.

J. Mech. Des 140(2), 022302 (Dec 11, 2017) (19 pages) Paper No: MD-17-1348; doi: 10.1115/1.4038300 History: Received May 17, 2017; Revised October 07, 2017

Additive manufacturing allows a direct fabrication of any sophisticated mechanism when the clearance of each joint is sufficiently large to compensate the fabrication error, which frees the designers of cumbersome assembly jobs. Clearance design for assembly mechanism whose parts are fabricated by subtractive manufacturing has been well defined. However, the related standard for parts fabricated by additive manufacturing is still under exploration due to the fabrication error and the diversity of printing materials. For saving time and materials in a design process, a designer may fabricate a series of small mechanisms to examine their functionality before the final fabrication of a large mechanism. As a mechanism is scaled, its joint clearances may be reduced, which affects the kinematics of the mechanisms. Maintaining certain clearance for the joints during the scaling process, especially for gear mechanisms, is an intricate problem involving the analysis of nonlinear systems. In this paper, we focus on the parametric design problem for the major types of joints, which allows the mechanisms to be scaled to an arbitrary level while maintaining their kinematics. Simulation and experimental results are present to validate our designs.

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Figures

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Fig. 1

Illustration of the major types of joints: (a) revolute joint, (b) universal joint, (c) prismatic joint, (d) spherical joint, and (e) gear joint (gear pair)

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Fig. 2

Illustration of the parameters of three major types of joints: (a) a revolute joint, (b) a prismatic joint, and (c) a spherical joint

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Fig. 3

Illustration of the parameters of a cylindrical spur gear: (a) the major parameters for determining the gear (refer to Table 1) and (b) pressure angle: the horizontal arrow indicates the velocity of the root of the arrow, and the other arrow indicates the counterforce of the pressure at the root of the arrow

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Fig. 4

Illustration of six closest matching teeth pairs

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Fig. 5

Illustration of scaling a gear mechanism with parameters m and z: (a) the original design, (b) m is doubled, (c) z is changed, and (d) both m and z are changed

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Fig. 6

Illustration of the coordinate frames OXYZ and OX1Y1Z1

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Fig. 7

Illustration of the critical parameters used for constructing involute and spiral curves in the OX1Y1Z1 frame

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Fig. 8

Constructing the spiral facets of a spiral bevel gear

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Fig. 9

Constructing a spiral bevel gear based on a tooth

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Fig. 10

Illustration of the six smallest shoulder clearances of a pair of spiral bevel gears

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Fig. 11

Illustration of scaling a prismatic joint with constant clearance: the scaling factors of the models in the second row and the third row are 1.5 and 2, respectively; the right column shows the corresponding cross section of the left column

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Fig. 12

Illustration of scaling a spherical joint with constant clearance: the scaling factors of the models in the second row and the third row are 1.5 and 2, respectively; the right column shows the corresponding cross section of the left column

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Fig. 13

Illustration of a two-stage gear reducer with cylindrical spur gears: the first column shows the mechanisms, the second column shows the shoulder clearances of the matching gears of the first stage, the third column shows the shoulder clearances of the matching gears of the second stage, and the fourth column shows the clearances of the revolute joints of each mechanism

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Fig. 14

Illustration of scaling a mechanism of straight bevel gears

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Fig. 15

Illustration of scaling a mechanism of spiral bevel gears

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Fig. 16

The change of minimum shoulder clearances as the gears rotate: the first row shows the performance of the two-stage reducer, where the curve with small magnitude and the curve with large magnitude indicate the changes of minimum shoulder clearances for the first stage and the second stage, respectively; the second row shows the performance of the straight bevel gears; the third row shows the performance of the spiral bevel gears; the first column shows the performance of the small model; the second column shows the performance of middle model; and the third column shows the performance of the large model

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Fig. 17

Illustration of the fabricated mechanisms using spiral bevel gears

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Fig. 18

A close-up look of the shoulder clearances of the spiral bevel gear mechanisms, from left to right is the small, middle, and large gear mechanisms. The clearance is almost zero for the biting teeth.

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Fig. 19

Illustration of rotating the spiral gear mechanisms, on the left corner of each photo is the displaying time of a video

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Fig. 20

A cross section of each 3D-printed spiral bevel gear mechanism. From left to right are the small model, the middle model, and the large model.

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Fig. 21

Construction of a reference curve by connecting involute AB with line segment BO

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Fig. 22

Illustration of constructing a closed reference curve O-B-A-D-C-O

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Fig. 23

Extending the reference closed curve into a 3D shape

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Fig. 24

Illustration of obtaining a copy of the wedge in Fig. 23 by rotating it by an angle of /z, where z is the number of teeth in the gear

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Fig. 25

Determining a tooth by U− U1 ∩ U2, where U1 is the addendum cylinder and U2 is the union of the two wedges (shown in transparent mode)

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Fig. 26

Illustration of constructing a gear: (a) calling a circular pattern geometry function of UG with the tooth obtained in Fig. 25 and the addendum cylinder and (b) calling a Boolean operation on the teeth and the addendum cylinder

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Fig. 27

Involute A1B1 and involute A2B2 in their coordinate frames

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Fig. 28

Transforming coordinate frames x1o1y1 and x2o2y2 into a common coordinate frame xoy

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Fig. 29

Computing the shoulder clearance h1 between g1 and g2

Tables

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