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Research Papers

Three-Position Synthesis of Origami-Evolved, Spherically Constrained Spatial Revolute–Revolute Chains

[+] Author and Article Information
Kassim Abdul-Sater

Institute of Micro Technology and
Medical Device Technology,
Faculty of Mechanical Engineering,
Technische Universität München,
Garching 85748, Germany
e-mail: kassim.abdul-sater@tum.de

Manuel M. Winkler

Institute of Micro Technology and
Medical Device Technology,
Faculty of Mechanical Engineering,
Technische Universität München,
Garching 85748, Germany
e-mail: manuel.winkler@tum.de

Franz Irlinger

Institute of Micro Technology and
Medical Device Technology,
Faculty of Mechanical Engineering,
Technische Universität München,
Garching 85748, Germany
e-mail: irlinger@tum.de

Tim C. Lueth

Institute of Micro Technology and
Medical Device Technology,
Faculty of Mechanical Engineering,
Technische Universität München,
Garching 85748, Germany
e-mail: Tim.lueth@tum.de

1Corresponding author.

Manuscript received November 13, 2014; final manuscript received March 20, 2015; published online August 18, 2015. Assoc. Editor: Larry L. Howell.

J. Mechanisms Robotics 8(1), 011012 (Aug 18, 2015) (11 pages) Paper No: JMR-14-1320; doi: 10.1115/1.4030370 History: Received November 13, 2014

This paper presents a finite position synthesis (f.p.s.) procedure of a spatial single-degree-of-freedom linkage that we call origami-evolved, spherically constrained spatial revolute–revolute (RR) chain here. This terminology is chosen because the linkage may be found from the mechanism equivalent of an origami folding pattern, namely, known as the Miura-ori folding. As shown in an earlier work, the linkage under consideration has naturally given slim shape and essentially represents two specifically coupled spherical four-bar linkages, whose links may be identified with spherical and spatial RR chains. This provides a way to apply the well-developed f.p.s. theory of these linkage building blocks in order to design the origami-evolved linkage for a specific task. The result is a spherically constrained spatial RR chain, whose end effector may reach three finitely separated task positions. Due to an underspecified spherical design problem, the procedure provides several free design parameters. These can be varied in order to match further given requirements of the task. This is shown in a design example with particularly challenging space requirements, which can be fulfilled due to the naturally given slim shape.

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Figures

Grahic Jump Location
Fig. 1

Steps that evolve the family of origami-evolved, spherically constrained planar, spherical, and spatial RR chains from the Miura-ori folding pattern

Grahic Jump Location
Fig. 2

Geometric parameters at the origami-evolved, spherically constrained spatial RR chain required for synthesis

Grahic Jump Location
Fig. 3

The spatial RR chain, defined by two skew revolute joint axes

Grahic Jump Location
Fig. 4

Example of a synthesized Bennett linkage, obtained from three-position synthesis solutions

Grahic Jump Location
Fig. 5

Different cases that define the calculation of ρy using Eq. (12). The rotation direction corresponds to (Y(ρy))T.

Grahic Jump Location
Fig. 6

Different cases that define the calculation of θi using Eq. (15). The rotation direction corresponds to (X(θi))T.

Grahic Jump Location
Fig. 7

Frame B˜' as well as angles involved in the inverse kinematics calculations

Grahic Jump Location
Fig. 8

Origami-evolved, spherically constrained spatial RR chain reaching the three-position from Table 1

Grahic Jump Location
Fig. 9

Three-position spatial car door guidance task: back, front, and side view

Grahic Jump Location
Fig. 10

Space limitations for the linkage in configuration i = 1

Grahic Jump Location
Fig. 11

Revolute joint axes of the spatial RR guiding chain obtained from a variation of task angles {ψ3,ϑ3,ϕ3} in a range of ± 8 deg

Grahic Jump Location
Fig. 12

The intersection of ray and triangle

Grahic Jump Location
Fig. 13

Final collision-free design in the stowed compact reference configuration

Grahic Jump Location
Fig. 14

The origami-evolved, spherically constrained spatial RR chain reaching the three task positions

Grahic Jump Location
Fig. 15

Selective laser sintering rapid prototyping model of the origami-evolved car door guidance linkage

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