Research Papers

Design Exploration and Kinematic Tuning of a Power Modulating Jumping Monopod

[+] Author and Article Information
Mark M. Plecnik

Biomimetic Millisystems Lab,
Department of Electrical Engineering and
Computer Sciences,
University of California,
Berkeley, CA 94720
e-mail: mplecnik@berkeley.edu

Duncan W. Haldane

Biomimetic Millisystems Lab,
Department of Mechanical Engineering,
University of California,
Berkeley, CA 94720
e-mail: dhaldane@berkeley.edu

Justin K. Yim

Biomimetic Millisystems Lab,
Department of Electrical Engineering and
Computer Sciences,
University of California,
Berkeley, CA 94720
e-mail: yim@eecs.berkeley.edu

Ronald S. Fearing

Biomimetic Millisystems Lab,
Department of Electrical Engineering and
Computer Sciences,
University of California,
Berkeley, CA 94720
e-mail: ronf@eecs.berkeley.edu

1Corresponding author.

Manuscript received April 29, 2016; final manuscript received October 27, 2016; published online December 7, 2016. Assoc. Editor: Sarah Bergbreiter.

J. Mechanisms Robotics 9(1), 011009 (Dec 07, 2016) (13 pages) Paper No: JMR-16-1123; doi: 10.1115/1.4035117 History: Received April 29, 2016; Revised October 27, 2016

The leg mechanism of the novel jumping robot, Salto, is designed to achieve multiple functions during the sub-200 ms time span that the leg interacts with the ground, including minimizing impulse loading, balancing angular momentum, and manipulating power output of the robot's series-elastic actuator. This is all accomplished passively with a single degree-of-freedom linkage that has a coupled, unintuitive design which was synthesized using the technique described in this paper. Power delivered through the mechanism is increased beyond the motor's limit by using variable mechanical advantage to modulate energy storage and release in a series-elastic actuator. This power modulating behavior may enable high amplitude, high frequency jumps. We aim to achieve all required behaviors with a linkage composed only of revolute joints, simplifying the robot's hardware but necessitating a complex design procedure since there are no pre-existing solutions. The synthesis procedure has two phases: (1) design exploration to initially compile linkage candidates, and (2) kinematic tuning to incorporate power modulating characteristics and ensure an impulse-limited, rotation-free jump motion. The final design is an eight-bar linkage with a stroke greater than half the robot's total height that produces a simulated maximum jump power 3.6 times greater than its motor's limit. A 0.27 m tall prototype is shown to exhibit minimal pitch rotations during meter high test jumps.

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Grahic Jump Location
Fig. 3

A parameterization of a six-bar linkage that results in 11 design parameters

Grahic Jump Location
Fig. 2

The design process consists of design exploration and kinematic tuning phases

Grahic Jump Location
Fig. 1

The leg design of Salto transforms motor torque into a tuned vertical ground reaction force

Grahic Jump Location
Fig. 4

Four types of Stephenson path generating six-bars: (a) Stephenson I, (b) Stephenson II (binary), (c) Stephenson II (ternary), and (d) Stephenson III

Grahic Jump Location
Fig. 7

A six-bar linkage defined by coordinates A, B, C, D, F, G, H, and P0 drawn in configuration j

Grahic Jump Location
Fig. 5

Samples from an atlas of straight-line six-bars. Stephenson I types are shown in (a) and (b); Stephenson II (binary) types are shown in (c) and (d); Stephenson II (ternary) types are shown in (e) and (f); and Stephenson III types are shown in (g) and (h).

Grahic Jump Location
Fig. 6

Samples from an expanded atlas of Stephenson II (ternary) six-bars. The line-of-action was shifted to the left in (a) and shifted to the right in (b).

Grahic Jump Location
Fig. 13

An eight-bar linkage defined by coordinates A, B, C, D, F, G, H, K, L, M, and P0 drawn in configuration j

Grahic Jump Location
Fig. 14

Design iterations during the optimal design of an eight-bar linkage. Dimensions are in meters.

Grahic Jump Location
Fig. 8

Mechanical advantage is designed such that a decreasing spring torque is transformed into a constant vertical force pushing off the ground

Grahic Jump Location
Fig. 9

Design iterations during the optimal design of a six-bar linkage. Input link is colored in blue. Dimensions are in meters.

Grahic Jump Location
Fig. 10

(a) Mechanical advantage as a function of foot translation and (b) vertical GRF computed from dynamic simulation for select iterations of Figs. 9 and 14

Grahic Jump Location
Fig. 11

Time evolution of mechanical energy from simulations of Iterations IV and VIII (the final design)

Grahic Jump Location
Fig. 12

Angular momentum about the CM during simulated jumps with Iteration IV and Iteration VIII (the final design)

Grahic Jump Location
Fig. 15

Prototype monopod installed on a universal testing machine

Grahic Jump Location
Fig. 16

Mechanical advantage calculated from data measured by a universal testing machine compared to simulation of Iteration VIII. Experimental data show both compression and extension strokes.

Grahic Jump Location
Fig. 17

Composition of high speed footage for a spring-powered jump of 0.995 m



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