Kinematic synthesis of planar, shape-changing, rigid body mechanisms for design profiles with significant differences in arc length
This paper presents a kinematic procedure to synthesize planar mechanisms capable of approximating a shape change defined by a general set of curves. These “morphing curves,” referred to as design profiles, differ from each other by a combination of displacement in the plane, shape variation, and no...
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| Published in | Mechanism and machine theory Vol. 70; pp. 425 - 440 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.12.2013
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| Abstract | This paper presents a kinematic procedure to synthesize planar mechanisms capable of approximating a shape change defined by a general set of curves. These “morphing curves,” referred to as design profiles, differ from each other by a combination of displacement in the plane, shape variation, and notable differences in arc length. Where previous rigid-body shape-change work focused on mechanisms composed of rigid links and revolute joints to approximate curves of roughly equal arc length, this work introduces prismatic joints into the mechanisms in order to produce the different desired arc lengths. A method is presented to iteratively search along the profiles for locations that are best suited for prismatic joints. The result of this methodology is the creation of a chain of rigid bodies connected by revolute and prismatic joints that can approximate a set of design profiles.
•A procedure is developed for designing rigid-body, shape-changing mechanisms.•A chain of rigid bodies can be repositioned to approximate any number of curves.•The chain contains revolute and prismatic joints to match different length curves.•Theory is generated to compare contiguous sets of points among curves.•A process identifies the ideal shape for the rigid bodies and joint type/locations. |
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| AbstractList | This paper presents a kinematic procedure to synthesize planar mechanisms capable of approximating a shape change defined by a general set of curves. These "morphing curves," referred to as design profiles, differ from each other by a combination of displacement in the plane, shape variation, and notable differences in arc length. Where previous rigid-body shape-change work focused on mechanisms composed of rigid links and revolute joints to approximate curves of roughly equal arc length, this work introduces prismatic joints into the mechanisms in order to produce the different desired arc lengths. A method is presented to iteratively search along the profiles for locations that are best suited for prismatic joints. The result of this methodology is the creation of a chain of rigid bodies connected by revolute and prismatic joints that can approximate a set of design profiles. This paper presents a kinematic procedure to synthesize planar mechanisms capable of approximating a shape change defined by a general set of curves. These “morphing curves,” referred to as design profiles, differ from each other by a combination of displacement in the plane, shape variation, and notable differences in arc length. Where previous rigid-body shape-change work focused on mechanisms composed of rigid links and revolute joints to approximate curves of roughly equal arc length, this work introduces prismatic joints into the mechanisms in order to produce the different desired arc lengths. A method is presented to iteratively search along the profiles for locations that are best suited for prismatic joints. The result of this methodology is the creation of a chain of rigid bodies connected by revolute and prismatic joints that can approximate a set of design profiles. •A procedure is developed for designing rigid-body, shape-changing mechanisms.•A chain of rigid bodies can be repositioned to approximate any number of curves.•The chain contains revolute and prismatic joints to match different length curves.•Theory is generated to compare contiguous sets of points among curves.•A process identifies the ideal shape for the rigid bodies and joint type/locations. |
| Author | Shamsudin, Shamsul A. Myszka, David H. Murray, Andrew P. Schmiedeler, James P. |
| Author_xml | – sequence: 1 givenname: Shamsul A. surname: Shamsudin fullname: Shamsudin, Shamsul A. email: shamanuar@utem.edu organization: Faculty of Mechanical Engineering, Universiti Teknikal, Melaka, Malaysia – sequence: 2 givenname: Andrew P. surname: Murray fullname: Murray, Andrew P. email: amurray1@dayton.edu organization: Department of Mechanical and Aerospace Engineering, University of Dayton, Dayton, OH 45469, USA – sequence: 3 givenname: David H. surname: Myszka fullname: Myszka, David H. email: dmyszka@udayton.edu organization: Department of Mechanical and Aerospace Engineering, University of Dayton, Dayton, OH 45469, USA – sequence: 4 givenname: James P. surname: Schmiedeler fullname: Schmiedeler, James P. email: schmiedeler.4@nd.edu organization: Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA |
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| Cites_doi | 10.1016/S0094-114X(02)00035-6 10.1016/S0094-114X(99)00069-5 10.1016/j.mechmachtheory.2011.08.011 10.1016/j.matdes.2009.09.011 10.1115/1.3149843 10.1364/JOSAA.4.000629 10.1016/0094-114X(95)00055-4 10.1115/1.4004226 10.1088/0964-1726/5/6/010 10.1016/j.mechmachtheory.2011.07.008 10.1115/1.2829892 10.1109/34.88573 10.1016/j.mechmachtheory.2009.07.006 10.2514/1.29988 10.1177/1045389X08096734 10.1016/j.mechmachtheory.2006.04.014 10.1016/j.mechmachtheory.2011.01.009 10.1093/ptj/66.9.1365 10.1115/1.4007449 10.1016/0094-114X(78)90059-9 10.1109/TPAMI.1987.4767965 10.1016/S0262-8856(03)00137-9 10.1177/1045389X03035563 10.1109/8.8619 10.2514/1.C031060 10.1115/1.4005530 10.1115/1.2216735 10.1109/34.149591 |
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| Snippet | This paper presents a kinematic procedure to synthesize planar mechanisms capable of approximating a shape change defined by a general set of curves. These... |
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| SubjectTerms | Approximation Chains Displacement Image registration Kinematics Morphing Prismatic joints Rigid body mechanisms Rigid-body dynamics Shape-change Similarity transformation Synthesis Welded joints |
| Title | Kinematic synthesis of planar, shape-changing, rigid body mechanisms for design profiles with significant differences in arc length |
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