When a machine must provide unusual displacement or speed characteristics, don’t overlook noncircular gears. These oddly-shaped gears can fulfill several types of special motion requirements, and one of them may be the best solution for your application.

Why thease gears?

Various mechanical systems, such as cams and linkages, can provide special motion requirements, but noncircular gears often represent a simpler, more compact, or more accurate solution.

Servo systems may also be able to do the job, and they can be programmed to handle changing or complex functional requirements. But they are usually more expensive. Also some companies lack the expertise to solve problems with servo systems. Moreover, noncircular gears do offer limited ability to handle changing functional requirements. For example, you may be able to change an output function by adjusting the phase relationship between two mating noncircular gears.
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Some of the more common requirements handled by noncircular gears include converting a constant input speed into a variable output speed, and providing several different constant-speed segments during an operating cycle. Other applications require combined translation and rotation or stop-and-dwell motion. Here are a few examples that may stimulate some ideas about your own applications.

Variable speed
Several types of noncircular gears generate variable output speeds, particularly elliptical gears. Other, less commonly used types are triangular and square gears.

Elliptical: 

An ellipse is defined by a set of points such that the sum of the distances from two fixed points on its long axis to any point on the perimeter is a constant. This enables a set of like elliptical gears to run at a constant center distance but deliver an output speed that changes as they rotate. Elliptical gears come in two basic types: unilobe, which rotates about one of the fixed points, and bilobe, which rotates about the center. The speed-reduction (or increasing) ratio of these gears varies from 1/K to K, where K depends on the gear geometry, during each cycle of rotation. Practical values of K range up to 3 for a unilobe and up to 2 for a bilobe gear.

The largest radius of the driving gear mates with the smallest radius of the driven gear so that output speed is at its maximum. As the gears rotate, the radius of the driving gear gradually decreases and that of the driven gear increases, so speed decreases for the first ¼ revolution. Then the speed increases for the next ¼ revolution, etc. These periods of increasing or decreasing speed occur four times per revolution.
Elliptical gears are commonly used in packaging and conveyor applications.

Triangular:

A pair of triangular gears also converts constant input speed into alternating output speed. However, they have three lobes, or high points on the perimeter, rather than the two lobes in elliptical bilobe gears. As a result, triangular gears deliver six periods of speed increase or decrease per revolution, rather than four.

Square:

Gears that are square provide yet another way to produce varying output speed. These gears have four lobes, so they produce eight periods of speed increase or decrease per revolution.
Both triangular and square gears are limited to a smaller range of speed ratios than with elliptical gears.

Constant-speed segments

Where an application requires several constant-speed periods within a cycle, multispeed gears may be the answer. These gears make the transition between speeds by using special function segments on the gear perimeter, usually sinusoidal, between the constant-speed sections. Typically, the input and output gears are different.

Translation and rotation

For applications requiring both translational and rotational motion, certain gears serve as cam substitutes. These cam gears are often used in labeling machines. The cam gear duplicates the shape of a part to be labeled and a cam-following rack carries the labeling device at a constant surface speed. In welding applications, a cam gear simulates the shape of a part to be welded and a follower carries a welding torch at a constant speed to ensure uniform weld application.

Stop-and-dwell motion

Some machines must provide either stop-and-dwell, or reverse motion with a constant input speed. This is achieved by combining noncircular gears with round gears and a differential (epicyclic gear train). Using round gears with different ratios gives such an arrangement the flexibility of providing either stop-anddwell or reverse motion.

Stop-and-dwell motion is common in indexing mechanisms, where gears are used rather than cam or Geneva mechanisms. Reverse motion is required where a transfer device must operate between two locations. Here, a noncircular gear arrangement is usually simpler than a commonly used linkage assembly. Despite their flexibility, such arrangements tend to be expensive.

Typical applications

These examples show how noncircular gears solve manufacturing problems.

Sealing head: 

A heat-sealing device seals the tops of containers on a constant- speed conveyor. It must maintain contact for a short period of time (less than 1 sec) without slippage between the sealing head and container. A traditional approach is to install an indexing device that stops the conveyor while sealing occurs. Or, if the conveyor can’t be stopped, a cam and linkage device or electronic servo is used.

A simple solution involves mounting the sealing head on a crank mechanism driven by elliptical gears which let the head stay in contact with the container momentarily. A varying output speed provided by the gears lets the sealing head follow the container without slippage and then return for the next container.

Rotary cutoff knife: 

A rotary knife cuts material on a conveyor to different lengths while the conveyor runs at a fixed speed. To cut material of different lengths without changing the conveyor speed would require using different knife sizes (diameters) and changing the knife speed.

One solution is to drive the knife with elliptical or multispeed gears. Changing the input gear speed with respect to conveyor speed changes the length of material that is cut. Adjusting the phasing between gears relative to the cutoff point causes the knife to match the conveyor speed.

Conventional robots and machines are made of rigid materials that limit their ability to elastically deform and adapt their shape to external constraints and obstacles. Although they have the potential to be incredibly powerful and precise, these rigid robots tend to be highly specialized and rarely exhibit the rich multifunctionality of natural organisms.

However, as the field of robotics continues to expand beyond manufacturing and industrial automation and into the domains of healthcare, field exploration, and cooperative human assistance, robots and machines must become increasingly less rigid and specialized and instead approach the mechanical compliance and versatility of materials and organisms found in nature. As with their natural counterparts, this next generation of robots must be elastically soft and capable of safely interacting with humans or navigating through tightly constrained environments. Just as a mouse or octopus can squeeze through a small hole, a soft robot must be elastically deformable and capable of maneuvering through confined spaces without inducing damaging internal pressures and stress concentrations.

In contrast to conventional machines and robots, soft robots contain little or no rigid material and are instead primarily composed of fluids, gels, soft polymers, and other easily deformable matter. These materials exhibit many of the same elastic and rheological properties of soft biological matter and allow the robot to remain operational even as it is stretched and squeezed. Because of the near absence of rigid materials and its similarities to natural organisms, soft robots may be considered a subdomain of the more general fields of softmatter engineering or biologically inspired engineering. However, whereas these existing fields can be defined by their scientific foundations in soft-matter physics and biology, respectively, the emerging field of soft robotics remains open and free of dogmatic restrictions to any constrained set of methods, principles, or application domains. Instead, soft robotics represents an exciting new paradigm in engineering that challenges us to reexamine the materials and mechanisms that we use to make machines and robots so that they are more versatile, lifelike, and compatible for human interaction.

The promise of soft robots is perhaps best realized in environments and applications that require interaction with soft materials and organisms and/or the artificial replication of biological functionalities. For example, whereas industrial robots typically handle metals, hard plastics, semiconductors, and other rigid materials, medical robots will primarily interact with soft materials such as natural skin, muscle tissue, and delicate internal organs. Likewise, biologically inspired robots for field exploration and disaster relief will often encounter easily deformable surfaces like sand, mud, and soft soil. To prevent the robot from penetrating into the surface and causing damage or mechanical immobilization, the forces transferred between the robot and surface must be evenly distributed over a large contact area. This requires compliance matching—that is, the principle that contacting materials should share similar mechanical rigidity in order to evenly distribute internal load and minimize interfacial stress concentrations.

One measure of material rigidity is the modulus of elasticity, or Young’s modulus—a quantity that scales with the ratio of force to percent elongation of a prismatic bar that is stretched along its principal axis. Young’s modulus is only defined for homogenous, prismatic bars that are subject to axial loading and small deformations (< 0.2% elongation for metals) and thus has limited relevance to soft robots and other soft-matter technologies that have irregular (nonprismatic) shape and undergo large elastic or inelastic deformations. Nonetheless, Young’s modulus is a useful measure for comparing the rigidity of the materials that go into a soft robot. Most conventional robots are composed of materials such as metals and hard plastics that have a modulus of greater than 109 Pa = 109 N/m2. In contrast, most of the materials in natural organisms, such as skin and muscle tissue, have a modulus on the order of 102–106 Pa. That is, the materials in natural organisms are 3–10 orders of magnitude less rigid than the materials in conventional robots. This dramatic mismatch in mechanical compliance is a big reason why rigid robots are often biologically incompatible and even dangerous for intimate human interaction and rarely exhibit the rich multifunctionality and elastic versatility of natural organisms.

There are various materials used to build soft robots. Electroactive polymers (EAP) are often used as artificial muscles. Whole robots are usually made of multiple of these muscle-like actuators. EAPs are a branch of polymers that can contract and bend under applied voltage. They have lot of features that suit them for soft robotics. They can be made in any shape, are elastic, low weight and have large actuation strain. Also, very useful is an ability of EAPs to sense how much stretched they are. This is important when calculating (or ‘sensing’) the shape or the state of a robot’s body.

Other kind of soft actuators are the pneumatic artificial muscles (PAMs). These are basically soft tubes with inflexible fiber mesh reinforcement in the wall of the tube or on its surface. When air is pumped in, the tube expands in its diameter and shrinks in longitudinal axis because the fiber cannot stretch. There is also an extensor PAM actuator in which the mesh is placed differently, so the tube extends only in longitudinal axis when pressurized.
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controlling soft robots is rather hard. First part of the problem is to determine the actual position and shape of a robot. In case of hard robots it is quite easy to determine its shape, as we know where the DoFs (joints) are. We only need to know the angle of each joint and then calculate the position. Soft robots have infinite number of DoFs, however, there is always a finite number of sensors and actuators (muscles) in their bodies. Therefore it is impossible to have information about the state of each of the DoFs. Possible solution is determining the position of robot’s body parts from outside, using visual information, when the robot would have camera to see the actual situation. Next part of the problem is determining what actions the robot should do to get in the desired positon. To determine the shape of a robot from internal and external forces, multiple physical models have to be employed, namely models for solid and fluid mechanics, kinematics, electro-mechanics, thermodynamics and chemical kinetics. Simulating behavior of a continuum is, however, complicated problem demanding a lot of computational power. Sensing, control and path planning are main problems of today’s soft robotics.