Classes of Mechanisms

All types of compliant mechanism share remarkable flexibility, elasticity, displacement precision, specifically controlled compliance, comparative strength, and shape adaptability. The Compliant Systems Design Laboratory has developed various design methods, performance metrics, and applications of a number of them.

Compliant mechanisms are organized by class based on a number of criteria, including the way they distribute compliance, how they interact and coordinate movement of their various components, how they handle and control force loads exerted on them, and how those applied forces cause desired mortion and shape-morphing against external loads.

Lumped Compliance

Complaint mechanisms consisting of thin flexural hinges, replacing a conventional hinge joint, can be categorized as “lumped” complaint mechanisms and are prone to high stress concentrations since the flexion is concentrated in thin/narrow sections. Such a design works well as long as the mechanism is not subjected to heavy loads.

Flexural Joints

Flexural Joints

Basic flexural joints, or flexures, are sometimes referred to as “living hinges”. Unlike the other classes of compliant mechanism, a simple flexure focuses compliance along a single axis and location within the object body (lumped compliance). Design of such joints provides sufficient material to sustain appropriate levels of repeatability in a single plane and sufficient precision to insure that displacement is accurate and consistent for every use.

Since flexion is concentrated at localized zones, flexural joints exhibit very limited load-carrying capacity and are not suitable for applications that require moderate to heavy loads.


Single-use Hemostats, Forceps and other Surgical Clamps — provide a satisfactory performance alternative to metal instruments and yet are inexpensive enough to be discarded after a single use. These mechanisms are designed with a high level of accuracy to generate targeted clamping forces in specific profiles without damage to surrounding tissues. The design also allows for single use applications where, once actuated, the joint is permanently engaged (set and forget).

Distributed Compliance

Distributed Compliance

We are already familiar with a number of human-designed monoform compliant mechanisms that demonstrate distributed compliance. Perhaps the earliest and most elegantly example is an archer’s bow. As the archer draws the bow, its form changes in compliance to the drawn bowstring. This strong, flexible mechanism can be used with precision a good many times without failure. It can do this because, unlike the plastic bottle cap where the thin “flexural hinge” lumps stresses along a designated axis between rigid adjacent structures, the archer’s bow has no such localized flexural zones and distributes the stresses throughout its whole body. The Distributed Compliance concept was pioneered by CSDL and has been the primary focus of our labs’ research activities. Distributed compliance gives a structural system the ability to be simultaneously flexible and strong.

This simple and elegant compliant iris shows both how a monoform can achieve amazingly complex morphing, and also demonstrates what we call “distributed compliance”. As force is applied to points on the perimeter ring, each internal element is subject to equal, small, linear elastic strains (to maximize fatigue life), and yet, together, these elements generate large deformations to change the aperture geometry by 1000%!


Compliant Joints with Distributed Compliance

Translation Revolute Universal Joints

To overcome the drawbacks of some flexural joints, we have developed compliant joints that offer high load bearing capacity, low stress concentration, large range of motion, minimum axis drift, and very high off-axis stiffness. Various complaint joints with distributed compliance are being studied by CSDL and these include a compliant revolute joint, compliant universal joint (two revolute degrees of freedom), compliant spherical joint (3 revolute degrees of freedom) and compliant translational joint (2D and 3D).


Large Displacement Compliant Joints
Moon Y-M, Kota S., Trease B. (2000)

Embedded Sensing
Peshkin M, Northwestern U. Kota S., U. Michigan


  • Embedding a distributed sensor into a complaint universal joint serves as a low-cost but high precision joystick.
  • Various compliant joints are used in the construction of parallel kinematic machines for low-cost, high precision motion control.
  • A lightweight prosthetic wrist with compliant universal joint (made of composites) exhibits the same strength as a conventional universal joint made of steel but weighs less than 50% as much and benefits from absence of wear, lubrication, and maintenance.

Compliant Joints

Non-Linear Springs

Non-linear Springs

We have developed a generalized synthesis methodology, including topology, size, and shape optimization, for creating nonlinear springs for any prescribed load-displacement functions. Examples include but are not limited to a constant fore spring, or a stiffening spring with a J-shaped load-displacement function etc. Geometric nonlinearities of compliant mechanisms are exploited to generate nonlinear behavior in compliant mechanisms.


A Strength Based Approach for the Synthesis of a Compliant Nonlinear Spring for an Orthotic Knee Brace
Proceedings of 2013 ASME-IDETC conference, Krishnan G., Rank R., Rokosz J., Carvey P., Kota S. (2013)

Design of Single, Multiple, and Scaled Nonlinear Springs for Prescribed Non-linear Responses
ASME Journal of Mechanical Design, Jutte C.V., Kota S. (2009)

Topology Synthesis of Compliant Mechanisms Using Non-linear Beam Elements, Mechanics of Structures and Machines
Joo J., Kota S. (2003)


  • An automobile seat consisting of a 4-inch thick cushion was replaced by a pair of non-linear springs that match the load-displacement profile (similar to a J-shaped curve) of a thick cushion […with what benefits ?].
  • In prosthetics and artificial implants, nonlinear springs can approximate the nonlinear stress-strain “J”-curve of many biological materials. In MEMS devices, nonlinear hardening and softening springs can improve the performance of bandpass filters. At the macro scale, the inclusion of nonlinear potential energy also improves the crashworthiness of vehicles and aid in shock absorption.

Non-linear Springs

Multi-Stable Mechanisms

Multi Stable Mechanisms

Compliant mechanisms with multiple low potential energy (or stable) positions offer significant benefits over conventional detent schemes. A light switch is a bi-stable mechanism where no external energy is needed to maintain the mechanism in its stable (on/off) positions. We have developed a generalized method of synthesizing bistable and multi-stable mechanisms by combining multiple bi-stable mechanisms.


Synthesis of Multi-stable Compliant Mechanisms using Combinations of Bi-Stable Mechanisms
ASME Transactions, Journal of Mechanical Design, Oh Y., Kota S. (2009)


  • A quadri-stable (stable in four positions) rotational switch [for… ?]
  • An automobile trunk lid lock mechanism with multiple links, joints and springs was replaced by a bi-stable mechanism actuated by a monoform compliant mechanism that greatly reduces the sub-assembly cost and weight of the device.

Multi-stable Mechanisms

Compliant Parallel Kinematic Machines

CPKM Samples

Compliant Parallel Kinematic Machines (CPKMs) are similar to conventional PKMs except that conventional joints are replaced by large-displacement compliant joints with distributed compliance. Since compliant joints provide backlash-free motion, very high positioning accuracy can be obtained even with low precision actuators. We developed a mathematical method (using dual vectors and dual algebra) of synthesis of CPKMs


Design of Compliant Parallel Kinematic Machines
Proceedings of DETC, 27th Biannual Mechanisms and Robotics Conference, Moon Y.M., Kota S. (2002)


  • A CPKM with two rotational degrees of freedom serves as a module to convert a 3-axis CNC machine into a five-axis machine.
  • Flexible Passive Coupling Device — such as a docking collar with translational joints

Compliant Parallel Kinematic Machines

Elasto-Fluidic Devices

Elasto-fluidic systems use fluid displacement and material deformation to produce distributed force and motion. By manipulating fluid displacement within a flexible elastomeric envelope, their motions and structures are able to perform complex motions while conforming to the environment they are interacting with. And, since such components and pressures are “soft” compared to typical robotic elements they are potentially able to work safely alongside people. Devices using this form of mechanism have many biological parallels (e.g. elephant trunks, plant tendrils, muscular hydrostats) and so these designs offer a promising new direction in mechanism research.

Using fibers in pure tension and fluids in pure compression, our Fiber Reinforced Elastomeric Enclosures (FREEs) represent an extreme example of a complaint mechanism. FREEs provide advantages in material utilization, force production, kinematics, and design compactness. By employing elastomers as fluid containing elements, the material and consequently weight of the device is substantially reduced.

By varying the fiber angles we discovered a vast array of FREE actuators that are capable of extension/compression, axial rotation, bending, screw motions (combination of translation and rotation), and helical motions. The well-known McKibben actuator with two set of fibers at +/- 54 degrees for extension/compression motion occupy a single point in the entire design space (range of possibilities) we discovered. We design and tested hundreds of FREEs to characterize their kinematics, force, moment, and volume transduction properties. Analytical models were verified with experimental results.



Force and moment generation of fiber-reinforced pneumatic soft actuators
Intelligent Robots and Systems (IROS), 2013 IEEE/RSJ International Conference on. IEEE, Bishop-Moser J., Krishnan G., Kota S. (2013)

Force and hydraulic displacement amplification of fiber reinforced soft actuators
ASME conference Proceedings, Bishop-Moser J., Krishnan G., Kota S. (2013)

Towards snake-like soft robots: design of fluidic fiber-reinforced elastomeric helical manipulators
Intelligent Robots and Systems (IROS), 2013 IEEE/RSJ International Conference on. IEEE, Bishop-Moser J., Kota S. (2013)

Evaluating mobility behavior of fluid filled fiber-reinforced elastomeric enclosures
ASME Conference Proceedings, Krishnan G., Bishop-Moser J., Kim C., Kota S. (2012)

Kinematic synthesis of fiber reinforced soft actuators in parallel combinations
ASME Conference Proceedings, Bishop-Moser J., Krishnan G., Kim C., Kota S. (2012)

Design of soft robotic actuators using fluid-filled fiber-reinforced elastomeric enclosures in parallel combinations
Intelligent Robots and Systems (IROS), 2012 IEEE/RSJ International Conference on, pages 4264–4269, IEEE, Bishop-Moser J., Krishnan G., Kim C., Kota S. (2012)

Kinematic Synthesis of Fiber Reinforced Soft Actuators in Parallel Combination
Proceedings of ASME IDETC, Bishop-Moser J., Krishnan G., Kim C., Kota S. (2012)

Evaluating Mobility Behavior of Fluid Filled Fiber-Reinforced Elastomeric Enclosures
Proceedings of ASME IDETC, Krishnan G., Bishop-Moser J., Kim C., Kota S. (2012)

Design of Soft Robotic Actuators using Fluid Filled Fiber-Reinforced Elastomeric Enclosures
Bishop-Moser J., Krishnan G., Kim C., Kota S. (2012)


Soft Robotics — also known as continuum robots, incorporate fluid displacement as a driving force and fiber reinforced elastomeric enclosures as the transmission device. Soft robots with immense dexterity and power density can be created even at very small scales. Using a diverse range of asymmetric fiber orientations and serial/parallel configurations, many different robotic applications, both mobile and stationary, are possible.

Bio-Inspired Compliant Systems — such as snake-like soft robots that can form helix motions present many possible moving, grasping and climbing applications. Similar organic structures are ubiquitous in nature from starfishes to octopus tentacles to vines and tendrils. Other possibilities include annular arrangements of FREEs to create natural pumps and forms of locomotion. Still others might employ parallel arrays of elastomeric elements for multi-legged robots.

Soft Robotics and FREEs

Soft Robotics MEMS Applications Shape Morphing Design for No-Assembly Compliant Joints Medical Devices