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Research Papers

A Statically Unstable Passive Hopper: Design Evolution

[+] Author and Article Information
Peter Steinkamp

Casey Eye Institute,
Oregon Health and Science University,
3375 SW Terwilliger Boulevard,
Portland, OR 97239
e-mail: stein@ohsu.edu

Manuscript received September 8, 2016; final manuscript received November 8, 2016; published online January 13, 2017. Assoc. Editor: James Schmiedeler.

J. Mechanisms Robotics 9(1), 011016 (Jan 13, 2017) (7 pages) Paper No: JMR-16-1264; doi: 10.1115/1.4035222 History: Received September 08, 2016; Revised November 08, 2016

I have designed a sequence of gravity-powered passive-dynamic toys. These explore locomotion in general and hopping in particular. As with walking, running, crawling, etc., for animals, locomotion in these devices is a horizontal translation by means of approximately periodic patterns of motion. These toys were developed using intuitively guided trial-and-error design iteration based on live viewing, sound sequences, and review of slow motion video. A series of statically stable mechanisms is described. A progression of designs led to the central result: a monopod hopper that repeatedly hops more than 70 steps down a ramp, without conventional feedback control, fast spinning parts, or sensing means, yet unlike the previously statically stable designs, it cannot stand still stably. This free hopping was facilitated by a special mass distribution, and a spring that allowed relative translation and rotation between the body and leg. A retrospective evaluation reveals similarities to the morphology and gaits of hopping bipeds. These toys, interesting dynamical systems in any case, highlight the possibility of a significant role of mechanical structure in locomotion.

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References

Figures

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Fig. 1

U.S. Patent drawings of passive dynamic toys. (a) The passive dynamic ramp toy known as the Wilson Walkie, as well as a photograph of the toy. (b) The Slinky, another passive dynamic toy capable of walking down stairs. (c) A woodpecker toy that descends a pole using in a piecewise pecking motion.

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Fig. 2

Ball and car toy. A toy car A is attached by a curved wire spring B to highly elastic rubber ball C. One end of the wirespring is embedded in the ball. The opposing end of the wire spring is attached by hinge D to the top of the toy car. The lower panel shows the approximate orientation of ball during one hop cycle, as the car leads the ball down the hill. Arrows indicate the alternating direction of ball pitching between collisions (multimedia extension 2 video).

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Fig. 3

Curved foot hopping toy. A ramp-descending toy composed of body mass A, coil spring B, and curved foot C is shown in cross section. The mass of A was much greater than that of the coil spring B, or foot C. The curved foot was formed from a thin stiff plastic sheet into a shallow hemisphere. The lower panel shows a hopping sequence from left to right, beginning with collision. Following collision, the spring is compressed while the mass rotates forward, compressing the spring to a greater degree on the forward edge. The foot rolls forward. During flight, this asymmetric spring force is released, causing slight counter-rotation of the entire device before landing at a forward position. This can be observed in the slow motion portion of the footage (multimedia extension 3 video).

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Fig. 4

Initial rubber band sprung hopper. Body A (plywood frame) was attached by rubber bands B1–B4 to leg C. The frame had much more mass than the leg. This suspension allowed three (in the plane) degrees-of-freedom between leg and body: vertical bounce, fore-aft leg swing and some, but relatively less, horizontal displacement. If B1 = B3 and B2 = B4, vertical compression did not cause rotation. If, e.g., B1 > B3 and B4 > B2, and have equal spring rest lengths, then large vertical compression caused a counterclockwise rotation, thus making compression and rotation coupled, at least for large motions. Initial experiments used a narrow foot. A subsequent version had a springy brass foot D, which helped sustain hopping motion, but also resulted in (undesirable) static stability (multimedia extension 4 video).

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Fig. 5

Early use of leaf spring in hopper. The body frame A was a U shaped bent aluminum extrusion. Leaf spring pair B connected dual wooden legs (chopsticks) C to the frame. The tail mast D was a wooden dowel with clay adhered at top. Clamps and clay were used as adjustable masses E1–E2 (multimedia extension 5 video).

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Fig. 6

Final form of the statically unstable hopper. Schematic (1) shows body frame A, leaf spring B, and leg C. Leg and frame were joined by leaf spring B. The tail mast D with small terminal mass D2 were adjustably attached to the frame. Mass E was adjustable and could also be secured in various positions as a means of positioning the net center of mass. Foot F was hemispheric rubber. Complete specifications are in Appendix B. Photographs were extracted from high speed video footage and show the full device (traveling from right to left) in flight (2), and in close-ups of the leg movement during a hop cycle (3–6). Flexure modes of the leaf spring are shown.

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Fig. 7

Statically unstable hopper details. Dimensions in centimeters. (a) Shows full view of hopper including mast. (b) Side detail with measurements and approximate center of mass location. (c) Front view of device with legs. (d) Close-up of two piece leaf spring arrangement. (e) Close up of rubber feet.

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