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mechanical engineering Mechanical engineering is the study of physical machines and mechanism (engineering), mechanisms that may involve force and movement. It is an engineering branch that combines engineering physics and engineering mathematics, mathematics principl ...
, a compliant mechanism is a flexible
mechanism Mechanism may refer to: *Mechanism (economics), a set of rules for a game designed to achieve a certain outcome **Mechanism design, the study of such mechanisms *Mechanism (engineering), rigid bodies connected by joints in order to accomplish a ...
that achieves force and motion transmission through
elastic Elastic is a word often used to describe or identify certain types of elastomer, Elastic (notion), elastic used in garments or stretch fabric, stretchable fabrics. Elastic may also refer to: Alternative name * Rubber band, ring-shaped band of rub ...
body deformation. It gains some or all of its motion from the relative flexibility of its members rather than from rigid-body
joints A joint or articulation (or articular surface) is the connection made between bones, ossicles, or other hard structures in the body which link an animal's skeletal system into a functional whole.Saladin, Ken. Anatomy & Physiology. 7th ed. McGraw- ...
alone. These may be monolithic (single-piece) or jointless structures. Some common devices that use compliant mechanisms are backpack latches and paper clips. One of the oldest examples of using compliant structures is the
bow and arrow The bow and arrow is a ranged weapon system consisting of an elasticity (physics), elastic launching device (bow) and long-shafted projectiles (arrows). Humans used bows and arrows for hunting and aggression long before recorded history, and the ...
. Compliant mechanisms manufactured in a plane that have motion emerging from said plane are known as lamina emergent mechanisms or LEMs.


Design methods

Compliant mechanism design continues to be an active area of research in the mid 2020s. Many methods have been developed for compliant mechanism design, broadly in two categories:


Kinematics approaches

Kinematic In physics, kinematics studies the geometrical aspects of motion of physical objects independent of forces that set them in motion. Constrained motion such as linked machine parts are also described as kinematics. Kinematics is concerned with s ...
synthesis regards compliant mechanisms as discrete combinations of rigid and compliant elements.


Pseudo-Rigid Body Model

The earliest kinematic approach relies on a pseudo- rigid-body model of the mechanism. In this model, flexible segments are modeled as rigid links connected to
revolute joint A revolute joint (also called pin joint or hinge joint) is a one-Degrees of freedom (mechanics), degree-of-freedom kinematic pair used frequently in Mechanism (engineering), mechanisms and machines. The joint Constraint (classical mechanics), co ...
s with torsional springs. Other structures can be modeled as a combination of rigid links, springs, and
damper A damper is a device that deadens, restrains, or depresses. It may refer to: Music * Damper pedal, a device that mutes musical tones, particularly in stringed instruments * A mute for various brass instruments Structure * Damper (flow), a mech ...
s.


Constraint-based design

In Freedom and Constraint Topology (FACT) and screw-theory-based synthesis, basic compliant elements are first defined and analyzed by their degrees of constraint before being used to construct complex compliant mechanisms.


Structural optimization approach

These approaches treat the entire structure of the mechanism as one compliant body. Computational methods are used for
topology optimization Topology optimization is a mathematical method that optimizes material layout within a given design space, for a given set of loads, boundary conditions and constraints with the goal of maximizing the performance of the system. Topology optimizat ...
of the structure. Expected loading and desired motion and force transmission are input and the system is optimized for weight, accuracy, and minimum stresses. More advanced methods first optimize the underlying linkage configuration and then optimize the topology around that configuration. Other optimization techniques focus topology optimization of the flexure joints by taking as input a rigid mechanism and replacing all the rigid joints with optimized flexure joints. To predict the behavior of the structure, finite-element stress analysis is done to find deformation and stresses over the entire structure.


Advantages

Compliant structures are often created as an alternative to similar mechanisms that use multiple parts. There are two main advantages for using compliant mechanisms: * Low cost: A compliant mechanism can usually be fabricated into a single structure, which is a dramatic simplification in the number of required parts. A single-piece compliant structure can be manufactured through injection molding, extrusion, and 3d printing, among other methods. This makes the manufacturing relatively cheap and accessible. * Better efficiency: Compliant mechanisms do not suffer from some issues that affect multi-bodied mechanisms, such as
backlash Backlash may refer to: Literature * '' Backlash: The Undeclared War Against American Women'', a 1991 book by Susan Faludi * ''Backlash'' (Star Wars novel), a 2010 novel by Aaron Allston * Backlash (Marc Slayton), a comic book character from ...
or surface wear. Due to the usage of flexible elements, compliant mechanisms can easily store energy to be released at a later time or transformed into other forms of energy.


Disadvantages

The full range of a mechanism depends on the material and geometry of the structure; due to the nature of flexure joints, no purely compliant mechanism can achieve continuous motion such as found in a normal joint. Also, the forces applied by the mechanism are limited to the loads the structural elements can withstand without failure. Due to the shape of flexure joints, they tend to be locations of stress concentration. This, combined with the fact that mechanisms tend to perform cyclic or periodic motion, can cause fatigue and eventual failure of the structure. Also, since some or all of the input energy is stored in the structure for some time, not all of this energy is released back as desired. However, this can be a desirable property to add damping to the system.


Applications

Some of the oldest uses of compliant structures date back to several millennia. One of the oldest examples is the bow and arrow. Some designs of
catapult A catapult is a ballistics, ballistic device used to launch a projectile at a great distance without the aid of gunpowder or other propellants – particularly various types of ancient and medieval siege engines. A catapult uses the sudden rel ...
s also made use of the flexibility of the arm to store and release energy to launch the projectile larger distances. Compliant mechanisms are used in a variety of fields such as adaptive structures and biomedical devices. Compliant mechanisms can be used to create
self-adaptive mechanisms Self-adaptive mechanisms, sometimes simply called adaptive mechanisms, in engineering, are underactuated mechanisms that can adapt to their environment. One of the most well-known example of this type of mechanisms are underactuated fingers, gripp ...
, commonly used for
grasp A grasp is an act of taking, holding or seizing firmly with (or as if with) the hand. An example of a grasp is the handshake, wherein two people grasp one of each other's like hands. In zoology Zoology ( , ) is the scientific study of an ...
ing in robotics. Since robots require high accuracy and have limited range, there has been extensive research in compliant robot mechanisms.
Microelectromechanical systems MEMS (micro-electromechanical systems) is the technology of microscopic devices incorporating both electronic and moving parts. MEMS are made up of components between 1 and 100 micrometres in size (i.e., 0.001 to 0.1 mm), and MEMS devices ...
are one of the main applications of compliant mechanisms. These systems benefit from the lack of required assembly and simple planar shape of the structure which can be easily manufactured using
photolithography Photolithography (also known as optical lithography) is a process used in the manufacturing of integrated circuits. It involves using light to transfer a pattern onto a substrate, typically a silicon wafer. The process begins with a photosensiti ...
. The ''flexible drive'' or ''resilient drive'', often used to
couple Couple or couples may refer to: *Couple, a set of two of items of a type *Couple (mechanics), a pair of force which are equal in magnitude but opposite in direction and separated by a perpendicular distance so that their line of action do not co ...
an
electric motor An electric motor is a machine that converts electrical energy into mechanical energy. Most electric motors operate through the interaction between the motor's magnetic field and electric current in a electromagnetic coil, wire winding to gene ...
to a machine (for example, a
pump A pump is a device that moves fluids (liquids or gases), or sometimes Slurry, slurries, by mechanical action, typically converted from electrical energy into hydraulic or pneumatic energy. Mechanical pumps serve in a wide range of application ...
), is one example. The drive consists of a rubber "spider" sandwiched between two metal
dogs The dog (''Canis familiaris'' or ''Canis lupus familiaris'') is a domesticated descendant of the gray wolf. Also called the domestic dog, it was selectively bred from a population of wolves during the Late Pleistocene by hunter-gatherers ...
. One dog is fixed to the motor
shaft Shaft may refer to: Rotating machine elements * Shaft (mechanical engineering), a rotating machine element used to transmit power * Line shaft, a power transmission system * Drive shaft, a shaft for transferring torque * Axle, a shaft around whi ...
and the other to the pump shaft. The flexibility of the rubber part compensates for any slight misalignment between the motor and the pump. See
rag joint A rag joint refers to certain flexible joints ( flexure bearings) found on automobiles and other machines. They are typically found on steering column shafts that connect the steering wheel to the steering gear input shaft, usually at the stee ...
and
giubo A ''giubo'' ( ; etymology: giunto Boschi, "Boschi joint"), also known as a 'flexdisc', and sometimes misspelled as guibo, is a flexible coupling used to transmit rotational torque between the drive shaft and the companion flange on mechanical de ...
.


Image gallery

File:AluStir - Kompliente Systeme in der Lasermaterialbearbeitung.jpg, A laser welding robot positions the workpieces by a compliant mechanism between table and fixture File:Compliant Iris mechanism - closed.png, Compliant Iris mechanism – closed File:Compliant Iris mechanism - open.png, Compliant Iris mechanism – open File:Compliant clip.png, Compliant clip File:Bistable compliant switch mechanism.png, Bistable compliant switch mechanism


See also

*
Stiffness Stiffness is the extent to which an object resists deformation in response to an applied force. The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is. Calculations The stiffness, k, of a ...
* Remote center compliance *
Living hinge A living hinge or integral hinge is a thin flexible hinge (flexure bearing) made from the same material as the two rigid pieces it connects. Description A living hinge or integral hinge is a thin flexible hinge (flexure bearing). It is made fr ...
*
Flexure bearing A flexure bearing is a category of flexure which is engineered to be compliant in one or more angular degrees of freedom. Flexure bearings are often part of compliant mechanisms. Flexure bearings serve much of the same function as conventional be ...
*
Self-adaptive mechanisms Self-adaptive mechanisms, sometimes simply called adaptive mechanisms, in engineering, are underactuated mechanisms that can adapt to their environment. One of the most well-known example of this type of mechanisms are underactuated fingers, gripp ...


References

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External links


Why Machines That Bend Are Better
YouTube YouTube is an American social media and online video sharing platform owned by Google. YouTube was founded on February 14, 2005, by Steve Chen, Chad Hurley, and Jawed Karim who were three former employees of PayPal. Headquartered in ...
video by
Veritasium Derek Alexander Muller (born 9 November 1982) is a Science communication, science communicator and media personality, best known for his YouTube channel Veritasium, which has over 17.8 million subscribers and 3.3 billion views as of April 2025. ...


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YouTube YouTube is an American social media and online video sharing platform owned by Google. YouTube was founded on February 14, 2005, by Steve Chen, Chad Hurley, and Jawed Karim who were three former employees of PayPal. Headquartered in ...
video - A Computational Design Tool for Compliant Mechanisms by Disney Research Hub

- BYU Compliant Mechanisms Research
Compliant Finray gripper for high-speed robotic electrical plug assembly
YouTube YouTube is an American social media and online video sharing platform owned by Google. YouTube was founded on February 14, 2005, by Steve Chen, Chad Hurley, and Jawed Karim who were three former employees of PayPal. Headquartered in ...
video Mechanisms (engineering)