Technical Brief

A Closed-Form Kinematic Model for Fiber-Reinforced Elastomeric Enclosures

[+] Author and Article Information
Wyatt Felt

Robotics and Motion Laboratory (RAMlab),
Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48105
e-mail: wfelt@umich.edu

C. David Remy

Robotics and Motion Laboratory (RAMlab),
Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48105
e-mail: cdremy@umich.edu

1Corresponding author.

Manuscript received March 31, 2017; final manuscript received September 26, 2017; published online November 23, 2017. Assoc. Editor: Hai-Jun Su.

J. Mechanisms Robotics 10(1), 014501 (Nov 23, 2017) (6 pages) Paper No: JMR-17-1082; doi: 10.1115/1.4038220 History: Received March 31, 2017; Revised September 26, 2017

In this work, we present a closed-form model, which describes the kinematics of fiber-reinforced elastomeric enclosures (FREEs). A FREE actuator consists of a thin elastomeric tube surrounded by reinforcing helical fibers. Previous models for the motion of FREEs have relied on the successive compositions of “instantaneous” kinematics or complex elastomer models. The model presented in this work classifies each FREE by the ratio of the length of its fibers. This ratio defines the behavior of the FREE regardless of the other parameters. With this ratio defined, the kinematic state of the FREE can then be completely described by one of the fiber angles. The simple, analytic nature of the model presented in this work facilitates the understanding and design of FREE actuators. We demonstrate the application of this model in an actuator design case study.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Daerden, F. , and Lefeber, D. , 2002, “ Pneumatic Artificial Muscles: Actuators for Robotics and Automation,” Eur. J. Mech. Environ. Eng., 47(1), pp. 11–21. http://citeseerx.ist.psu.edu/viewdoc/download?doi=
Agerholm, M. , and Lord, A. , 1961, “ The Artificial Muscle of Mckibben,” Lancet, 277(7178), pp. 660–661. [CrossRef]
Andrikopoulos, G. , Nikolakopoulos, G. , and Manesis, S. , 2011, “ A Survey on Applications of Pneumatic Artificial Muscles,” 19th Mediterranean Conference on Control Automation (MED), Corfu, Greece, June 20–23, pp. 1439–1446.
Bishop-Moser, J. L. , 2014, “ Design of Generalized Fiber-Reinforced Elasto-Fluidic Systems,” Ph.D. thesis, University of Michigan, Ann Arbor, MI. https://deepblue.lib.umich.edu/handle/2027.42/107202
Krishnan, G. , Bishop-Moser, J. , Kim, C. , and Kota, S. , 2015, “ Kinematics of a Generalized Class of Pneumatic Artificial Muscles,” ASME J. Mech. Rob., 7(4), p. 041014. [CrossRef]
Connolly, F. , Polygerinos, P. , Walsh, C. J. , and Bertoldi, K. , 2015, “ Mechanical Programming of Soft Actuators by Varying Fiber Angle,” Soft Rob., 2(1), pp. 26–32. [CrossRef]
Connolly, F. , Walsh, C. J. , and Bertoldi, K. , 2017, “ Automatic Design of Fiber-Reinforced Soft Actuators for Trajectory Matching,” Proc. Natl. Acad. Sci., 114(1), pp. 51–56. [CrossRef]
Sedal, A. , Bruder, D. , Bishop-Moser, J. , Vasudevan, R. , and Kota, S. , 2017, “ A Constitutive Model for Torsional Loads on Fluid-Driven Soft Robots,” ASME Paper No. DETC2017-67970.
Singh, G. , and Krishnan, G. , 2017, “ A Constrained Maximization Formulation to Analyze Deformation of Fiber Reinforced Elastomeric Actuators,” Smart Mater. Struct., 26(6), p. 065024. [CrossRef]
Chou, C.-P. , and Hannaford, B. , 1996, “ Measurement and Modeling of Mckibben Pneumatic Artificial Muscles,” IEEE Trans. Rob. Autom., 12(1), pp. 90–102. [CrossRef]
Singh, G. , and Krishnan, G. , 2015, “ An Isoperimetric Formulation to Predict Deformation Behavior of Pneumatic Fiber Reinforced Elastomeric Actuators,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Hamburg, Germany, Sept. 28–Oct. 2, pp. 1738–1743.
Gilbertson, M. D. , McDonald, G. , Korinek, G. , de Ven, J. D. V. , and Kowalewski, T. M. , 2017, “ Serially Actuated Locomotion for Soft Robots in Tube-Like Environments,” IEEE Rob. Autom. Lett., 2(2), pp. 1140–1147. [CrossRef]
Nakamura, T. , and Shinohara, H. , 2007, “ Position and Force Control Based on Mathematical Models of Pneumatic Artificial Muscles Reinforced by Straight Glass Fibers,” IEEE International Conference on Robotics and Automation (ICRA), Rome, Italy, Apr. 10–14, pp. 4361–4366.


Grahic Jump Location
Fig. 1

A FREE is a cylindrical soft pneumatic actuator. A FREE consists of an elastomeric tube surrounded by sets (or “families”) of identical helical fibers. The fibers in each family have the same angle with respect to the long axis (e.g., α) and the same unwound length (e.g., bα). Shown here are examples of two-fiber-family FREEs. The families are, respectively, described by the angles α and β. The unwound length of the helical fibers in each family, bα and bβ, remains constant, whereas the axial length l and diameter D change during actuation.

Grahic Jump Location
Fig. 2

The ratio 0<η=(bβ/bα)≤1 of the lengths of fibers in the two families determines the feasible angle combinations for a FREE actuator. The angle β can be used to specify the state of the actuator along the functional relationship of possible combinations. The locked manifold (dashed black line) is the set of angle combinations that maximize the volume of the actuator. When the volume of the actuator is increased by an internal pressure, the configuration of the actuator will advance toward the locked manifold. The gray regions of the figure are redundant and thus not specifically defined by this model. β is constrained to remain strictly less than α. Thus, when η = 1 (α = −β), β is constrained to be less than zero. This is indicated by the circle at the origin. The feasible region includes the lineα = −β but the line α = β is excluded. The values of η shownin this figure (and the others) are as follows: 1, 1516, 78, 1316, 34, 1116, 58, 916, 12, 716, 38, 516, 14, 316, 18, and 116.

Grahic Jump Location
Fig. 3

When the helices are planar circular arcs, the diameter is D0. Shown here are the paths of an α fiber and a β fiber for η = 0.5, n0,α = 0.5 and n0,β = −0.25.

Grahic Jump Location
Fig. 4

Examples of FREEs with the same bβ and D0 but different η levels at various values of β. For the actuators shown here, D0 is half of bβ. Each row corresponds to a value of η and each column a value of β.

Grahic Jump Location
Fig. 5

The length and diameter of FREE actuators for various values of η across β. The length of the actuator is the cosine function scaled by bβ and is always greatest at β = 0 (l = bβ). The diameter scales linearly with D0 and always increases with decreasing values of β. The maximum diameter is D0.

Grahic Jump Location
Fig. 6

The axial rotation of FREE actuators for various values of η across β. For η = 1 there is no rotation. The values shown here are normalized by n0,β. Note that n0,β=(−bβ/πD0).

Grahic Jump Location
Fig. 7

The volume of FREE actuators for various values of η across β. The volume values shown here are normalized by D02bβ. Each value of η corresponds to a unique angle βLM that maximizes the cylinder volume.

Grahic Jump Location
Fig. 8

The model can be used to design FREEs that meet specified kinematics. For instance, the FREE shown in this figure was designed to rotate a quarter turn while contracting 20%.




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In