mechanical design 101 - t1 introduction to kinematic synthesis · 2020. 6. 26. · me 322 kinematic...
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Introduction Kinematic Synthesis of Mechanisms
J. M. McCarthy and B. Roth
ME 322 Kinematic Synthesis of Mechanisms
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Watt: Drawing a Straight Line
ME 322 Kinematic Synthesis of Mechanisms
Watt’s straight-line linkage
James Watt: “Though I am not over anxious after fame, yet I am more proud of the parallel motion than of any other mechanical invention I have ever made.”
Dimensions of Watt’s linkage Use in high performance rear suspensions
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Four-bar Linkage Design
ME 322 Kinematic Synthesis of Mechanisms
Spare tire deployment
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Example Four-bar Linkages
ME 322 Kinematic Synthesis of Mechanisms
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More Four-bar Examples
ME 322 Kinematic Synthesis of Mechanisms
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Six-bar Linkage Design
ME 322 Kinematic Synthesis of Mechanisms
Long travel suspension
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Walking Machines
ME 322 Kinematic Synthesis of Mechanisms
Theo Jansen designed an eight-bar linkage for the legs of his Strandbeest
We can design a six-bar linkage with a similar walking gait
j x y
0 −5.160 −83.957
1 8.346 −84.026
2 21.993 −83.632
3 32.259 −82.128
4 33.018 −79.911
5 16.497 −73.889
6 −6.363 −62.120
7 −28.276 −74.865
8 −33.406 −80.964
9 −27.733 −83.440
10 −17.440 −84.032
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Different Gaits
ME 322 Kinematic Synthesis of Mechanisms
Here are results for other foot trajectories
Cognate linkages
Once the general homotopy is solved, parameter homotopies execute rapidly.
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Prototype
ME 322 Kinematic Synthesis of Mechanisms
One of the leg designs was manufactured as a compliant linkage
Lasercut polypropylene
Used to build a robot about 30 cm in length
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Mechanical Fourier Series
ME 322 Kinematic Synthesis of Mechanisms
1. A closed parameterized curve, f(t)=(x(t), y(t)), has a Fourier series expansion of the coordinate functions, x(t) and y(t); 2. Scotch yoke mechanisms generate cosine and sine terms, add using a belt and pulleys; 3. Combine the movements of x and y coordinates to draw the curve.
The Heart Curve
D. C. Miller, ``A 32-element Harmonic Synthesizer,’’ Journal of the Franklin Institute, Jan. 1916.
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Trigonometric Plane Curves
ME 322 Kinematic Synthesis of Mechanisms
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Epicycles: Coupled Serial Chain
ME 322 Kinematic Synthesis of Mechanisms
The Butterfly mechanism draws the Butterfly curve:
Y. Liu and J. M. McCarthy, "Design of Mechanisms to Draw Trigonometric Plane Curves," special issue “Selected Papers from the IDETC 2016,” Journal of Mechanisms and Robotics, April 2017, Vol 9(2). doi: 10.1115/1.4035882
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Manufacturing Prototype
ME 322 Kinematic Synthesis of Mechanisms
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A Linkage Writes in Chinese
ME 322 Kinematic Synthesis of Mechanisms
Each of the serial chains is driven by the same input.
The system has one degree-of-freedom
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Mechanical Driven Spatial Chains
ME 322 Kinematic Synthesis of Mechanisms
A TRR spatial chain was selected to model the magpie wing
TRR Chain TR Subchain
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Driving Six-bar Linkages
ME 322 Kinematic Synthesis of Mechanisms
The four target functions and the six-bar linkages that generate them
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Biomimetic Movement
ME 322 Kinematic Synthesis of Mechanisms
Solutions of the synthesis polynomials for each of the four target functions ψA=fA(ϕ), ψB=fB(ϕ), ψC=fC(ϕ), ψD=fD(ϕ)
BinaryDrivenψA ψB ψC ψD
Linkagesolutions 11428 7215 12870 11693
DesignCandidates 6068 4012 7363 577511pointmechanisms 0 0 3 010pointmechanisms 0 0 12 09pointmechanisms 0 7 95 48pointmechanisms 21 54 246 95Feasibledesigns 21 61 356 99
Synthesiscomputationtime(hr) 2.2 2.0 2.5 2.2Analysiscomputationtime(hr) 20.2 13.4 25.6 19.1
As many as 45x106 possible wing linkage designs.
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Hovering Wing Movement
ME 322 Kinematic Synthesis of Mechanisms
Balta,M.,Ahmed,K.A.,Wang,P.L.,McCarthy,J.M., and Taha, H. E., 2017. “Design and manufacturing of flapping wing mechanisms for micro air vehicles”. In 58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, p. 0509.
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Spatial Mechanisms
ME 322 Kinematic Synthesis of Mechanisms
O
AD
B E
C
F
R. S. Hartenberg and J. Denavit, 1964 Kinematic Synthesis of Linkages, McGraw-Hill, New York.
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Spatial Flapping Wing Mechanism
ME 322 Kinematic Synthesis of Mechanisms
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Flapping Wing Mechanism
ME 322 Kinematic Synthesis of Mechanisms
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Inventors
ME 322 Kinematic Synthesis of Mechanisms
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Summary
ME 322 Kinematic Synthesis of Mechanisms
Kinematic synthesis of mechanisms is the first step in the realization of devices to provide required movement and transmission of forces. Once this is defined, then material selection, stress analysis and dynamic analysis are used to shape the components to ensure performance and reliability.
Kinematic synthesis of robotic systems to draw curves contributes to design innovation. Opportunities are as varied as stroke rehabilitation, disaster relief, vehicle suspensions, and walking and flying robots.
Trigonometric cubic Bezier curves can be drawn by four-link coupled serial chains. Thus, a one degree-of-freedom linkage system can sign your name and write cursive Chinese.
Spatial Mechanism Synthesis is yielding innovative designs for new applications in areas as diverse as micro-air vehicles and tunnel boring machines.