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Sample Cutting Machine

What Is a Sample Cutting Machine?

A Sample Cutting Machine is a multi-cutting machine that can cut various materials into specified shapes.

When manufacturing a product, it is first necessary to create a shape at the prototype stage, but if mass production has not been decided or if the product is to be studied, a sample cutting machine is used to flexibly change the shape of the product without making a mold.

Since it can precisely cut various materials, sample cutters are used in the textile industry to cut fabrics, in the construction industry to cut insulation materials, and in the food industry to create shapes for confectionery, bread, and other products.

They are also sometimes used in combination with digital machine tools such as 3D printers. It can create three-dimensional objects at the prototype stage, enabling efficient and accurate prototype production.

The greatest advantage of a sample cutting machine is the flexibility to change the shape of the prototype without making a mold. This saves cost and time when the shape must be changed many times during the prototype stage or when the number of prototypes to be mass-produced is small. In addition, the ability to cut with a high degree of accuracy means that the shape of the prototype can be accurately reproduced.

The ability to create prototype shapes quickly and accurately makes it an excellent tool in terms of flexibility and cost. It contributes to improved productivity and faster R&D in various industries.

Uses of Sample Cutting Machine

Sample Cutting Machines are multi-cutting machines that can cut a variety of materials into specified shapes. They are used to make prototypes that have not yet been mass-produced, items that can only be made once, items that require precision that cannot be reproduced with a mold, and items whose shape needs to be confirmed for study purposes.

Because it can process all kinds of materials, including corrugated cardboard, paper, and foam materials, it is used in the corrugated/paper container industry, the chemical product industry, the heavy packaging industry, the building equipment industry, the bathroom, housing equipment, and renovation industry, and the sign and display industry, among others.

For example, in the corrugated industry, the sample cutting machine can be used to create boxes for a variety of uses, as there are many different box shapes. In the chemical products industry, materials such as plastic and resin are cut to create prototypes. Also, in the building equipment industry, it is used to make parts for furniture and interior decorations.

Because they can cut materials with high precision, sample cutters are used in the sign and display industry to create highly accurate letters and logos, and have a wide variety of uses.

Principle of Sample Cutting Machine

The principle of sample cutting machines consist of cutting by utilizing the resonance phenomenon by applying an external force synchronized with the natural frequency of an object.

The sample cutting machine consists of an oscillator and a transducer. The transducer has a piezoelectric element, and the AC voltage given to the piezoelectric element from the oscillator causes the blade to resonate. The cutter vibrates the blade at high speed in the longitudinal direction, enabling easy cutting without resistance even of materials that are difficult to cut with ordinary cutters.

Cutters emit virtually no swarf, smoke, noise, or sewage, making them an environmentally friendly cutting machine.

Sample cutting machines are often used to cut products in the prototype stage into shape. They are also suitable for making products for which mass production has not been decided, for which accuracy that cannot be reproduced with a mold is required, for which only one product is to be made, or for which the shape needs to be confirmed for study purposes.

Types of Sample Cutting Machine

There are two main types of sample cutting machines: Ultrasonic Cutters and Laser Cutters.

1. Ultrasonic Cutter

Ultrasonic cutters use ultrasonic waves to cut materials. It consists of an oscillator and a transducer. The transducer is cut by resonating the transducer using a piezoelectric element. They can cut with less resistance than conventional cutters and are environmentally friendly as they emit virtually no swarf, smoke, noise, or waste water. 

2. Laser Cutter

Laser cutters use lasers to cut materials. Because they can cut materials quickly and with high precision, they are used for a wide variety of materials, including plastics, fabrics, wood, and metals. When the laser beam is irradiated, the material evaporates, resulting in a very clean cut surface. It is also extremely safe and can be operated remotely, making it suitable for unmanned production.

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Sampler

What Is a Sampler?

A sampler is an abbreviation for a sampler bottle, made by Samplatech, and refers to bottles made of polypropylene, polyethylene, or fluoroplastic. They are not only highly transparent but also have excellent heat and chemical resistance.

They can be safely used for autoclaving.

Not only do they come in a variety of capacities, depending on the intended use. There are narrow-mouth and wide-mouth bottles.

Uses for Samplers

Sampler bottles are available in a variety of capacities, from small capacities to large capacities.

They are also available with narrow or wide mouths.

Samplers can be used not only in daily life but also in laboratories, chemical plants, and other factories, where they can hold everything from minute samples to a certain volume of liquid.

Principle of Samplers

Sampler bottles are extremely easy to work with because they have no inner stopper.

Some sampler bottles also have one-touch bottles that prioritize workability.

Those using polypropylene are made of a very transparent grade of polypropylene.

They are extremely durable, not only against acids but also against alkalis and some solvents.

Those manufactured with fluoropolymers can also be used for dry heat sterilization.

Some polyethylene products are also made from bioplastics derived from sugarcane. While maintaining the same quality as conventional polyethylene, these products are carbon-free because they are made from polyethylene derived from sugarcane.

This is because the raw material, sugarcane, absorbs carbon dioxide during its growth and photosynthesis, and although the sample bottles themselves do not decompose naturally, they are considered to have offset the carbon dioxide emitted when they are burned.

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Sand Pump

What Is a Sand Pump?

Sand pumps are used mainly at construction sites and river construction sites to suck up sludge and gravel.

However, sand pumps are equipped with a function that automatically prevents clogging, so they can be used safely even in areas with large amounts of sludge, gravel, or other impurities. Most sand pumps are more robust than normal pumps to prevent breakage when impurities are sucked in.

Uses of Sand Pumps

1. Mining and Excavation Industry

When mining ores and minerals, there is sometimes a mixture of earth, sand, and gravel. Sand pumps can pump slurries containing these solid particles and are used to transfer and process ores and minerals.

2. Construction

Construction sites generate large amounts of earth, sand, and gravel during foundation burial and drainage operations. Sand pumps are utilized to efficiently drain and transfer water and liquids containing these solid particles.

3. Marine Engineering

Sand pumps are also used to remove sediment and bedrock from the seafloor and during the construction of dikes and wharves. Pumping slurry from the seabed improves the efficiency of subsea construction.

4. Oil and Gas Industry

In oil and gas drilling operations, sand pumps are utilized to remove slurry generated in the borehole. They may also be used to process solid particles in wells.

5. Environmental Engineering

Sand pumps are also used in dredging operations in rivers and lakes, as well as in the cleanup of contaminated soil. They suck up the solid particles along with the liquid and transfer them to the treatment plant.

6. Agriculture

Agriculture requires the transfer and drainage of water and liquids. In particular, sand pumps are sometimes used in irrigation and drainage applications.

7. Industrial Applications

General industrial processes may also require the transfer of liquids containing solid particles. Sand pumps are used in such situations to increase production efficiency.

Principle of Sand Pumps

1. Suction

Sand pumps suck up slurry through a specially designed inlet located inside the pump. In this process, the space inside the pump is under negative pressure, and the surrounding liquid and solids are suctioned.

2. Transfer of Motion

The slurry is transferred through the pump. This transfer of motion is performed by parts and mechanisms inside the pump, which move the aspirated slurry in a forward direction.

3. Discharge

After the slurry has moved forward inside the pump, it is discharged through a specific outlet. In this process, the pressure near the outlet changes, causing the slurry to move outward, and the discharged slurry is sent to its destination.

4. Special Pump Design

Sand pumps are specially designed to handle solid particles efficiently. The internal construction and pump components are designed to be durable against the passage of slurry and the deposition of solids.

5. Energy Supply

Sand pumps require an energy supply source. It is commonly driven by an electric motor or engine, which creates movement and pressure changes inside the pump.

Types of Sand Pumps

1. Ejector Pump

Ejector pumps use a jet stream of water to suction and discharge slurry. The liquid is jetted at high speed to generate negative pressure and suction the slurry. The pump has a simple structure, yet can be operated efficiently.

2. Syringe Pump

Syringe pumps suck and discharge slurry through the movement of a syringe. It is suitable for applications where precise liquid control is required and minute flow rate adjustment is possible. They are often used in the medical field and laboratories.

3. Vacuum Pump

Vacuum pumps use a vacuum to suction slurry. By generating a vacuum, liquids and solids can be efficiently suctioned. They have high suction power and are suitable for a wide range of applications.

4. Seadan Pump

Seedan pumps are manual pumps used for suctioning slurry from containers. Slurry is suctioned and discharged by the movement of the cylinder and piston. Because of its simple operation, it is used for outdoor work.

5. Schropp Pump

Schropp pumps use a flow of water to suction slurry. The water flow suctions the slurry and discharges it through a dedicated pipe. Because it uses water flow, it is highly energy efficient.

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Sanding

What Is Sanding?

SandingsSanding is a process technique used to roughen the surface of an item. It is used on wood, metal, and plastic surfaces.

In the field of sports, sanding is also used to prepare surfaces for skiing, snowboarding, and surfing.

In this section, we will discuss sanding as it is used industrially.

Purpose of Sanding

Sanding is used on wood or wood products to improve the surface roughness of the surface to be used as a base surface for painting.

This is because uneven surface roughness prevents a uniform coating from being applied.

Therefore, sanding is performed to achieve a surface roughness that is appropriate for the properties of the paint.

In addition to smoothing the surface to facilitate the formation of the paint film, depending on the nature of the paint, the surface may be intentionally uneven to allow the paint to penetrate the unevenness and facilitate the formation of the paint film.

Another use of sanding is to adjust the texture of a material. For example, wood-plastic products, which are a mixture of resin and wood, are sanded to give the appearance of wood after injection molding.

Sanding Methods

Sanding can be done by hand or by machine.

1. Manual Sanding

In the case of manual sanding, the sanding paper is attached to the surface to be sanded, such as a sanding pad, and the surface is slid in the same direction with light pressure.

Sandpaper is numbered according to the roughness of the surface. The smaller the number marked on the sandpaper, the rougher the surface and the rougher the surface after sanding. Therefore, the first step is to process the surface with the roughest sandpaper, for example, about No. 80. This is done to eliminate irregularities on the wood surface and make the surface flat.

Then, we changed to a finer grit sanding paper to make the wood surface even.

The final step is to finish the surface with a finer grit sandpaper. Sanding is a technique to further polish the surface to a smooth finish.

When done by hand, the finish often depends on the skill of the operator.

2. Machine

For products that require mass production, sanding is done by machine, using a device called an electric sander.

Sanding is performed by rotating or sliding the surface to which the sandpaper is attached on the electric sander.

The time required for sandings can be reduced compared to manual sandings.

About Sandpaper

There are various types of sandpaper, and those used for wood, as mentioned above, and those used for metal and plastic, as mentioned above, are completely different.

It is important to use different types of sandpaper depending on the material used.

Conclusion

It is important to consider the material, application, and versatility of the product to be processed, to choose hand sanding or machine sanding, to determine the degree of sanding required, and to use the appropriate sandpaper for the material.

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Side Clamp

What Is a Side Clamp?

A side clamp, also known as a side push clamp, is a jig for cutting and is a clamping component that presses down on an object from the side.

It is used as a clamp when machining the top surface of an object.

The side clamp must be used in accordance with the shape of the object and the machining process to securely and firmly clamp the object while avoiding any interference between the object and the tool.

Uses of Side Clamps

The objects to be processed with a side clamp include a wide variety of shapes, such as small, thin, and irregularly shaped objects.

Side clamps are also required in many machining processes, such as roughing and finishing.

For example, when machining small objects, using other clamping parts may take up too much space, making it impossible to place more than planned.

In addition, when fixing thin objects, interference by tools can be a problem, but this can be prevented by using side clamps suitable for thin objects.

Principle of Side Clamps

Side clamps are based on the principle of leverage.

When a force is applied to the force point of side clamps, it is designed to transmit the force to the point of action so that it can be secured.

However, if too much force is applied to the fulcrum of the side clamps, the body of the clamp may be deformed, resulting in inadequate clamping force.

Also, if the object is clamped strongly from the side, it may be lifted and the target fixation accuracy may not be reached.

Some side clamps, however, prevent lifting by clamping the object diagonally downward.

This side clamp prevents the object from lifting during clamping, enabling high-precision machining.

Also, it is difficult to clamp odd-shaped objects, and it is time-consuming to make jigs for them.

Furthermore, side clamps are also available for soft materials such as aluminum and brass, which are easily damaged when clamped.

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Cleanroom Robots

What Are Cleanroom Robots?

Cleanroom robots are specialized robots designed for use in clean rooms. They are engineered to maintain a specific level of cleanliness within the clean room environment.

There are various types of cleanroom robots tailored to different applications and products.

These robots are deployed to automate tasks within clean rooms, where achieving a certain level of cleanliness may be challenging with human workers present. By using cleanroom robots, it becomes possible to maintain a high level of cleanliness while eliminating the need for human entry into the clean room, thus enabling the production of products under pristine conditions.

Applications of Cleanroom Robots

Cleanroom robots serve as replacements for tasks typically carried out by human workers in cleanroom environments.

In some cases, such as the food industry where relatively straightforward tasks are involved, clean robots are employed as labor-saving devices suitable for clean room use.

Conversely, in the semiconductor manufacturing sector, which demands the highest standards of cleanliness, Cleanroom robots enable the production of top-quality products with even stricter cleanliness standards, eliminating the need for human entry into clean rooms.

Features of Cleanroom Robots

Clean rooms used in handling food and semiconductor materials are isolated from external spaces, and their guaranteed cleanliness levels are defined during the design phase. This includes factors such as the performance and quantity of air filters utilized, as well as the location and capacity of air conditioning equipment.

Classifications are employed to denote cleanliness levels, with smaller class numbers indicating higher guaranteed cleanliness. This ranges from class 100 for semiconductor manufacturing to class 1000 to 10000 for facilities handling food products.

Any equipment installed in a clean room must, in principle, correspond to the specified class, as a cleanliness level below this standard can lead to quality control and quality assurance issues. Conventional machinery, including robots, is unsuitable for use as cleanroom robots, as dust generated by components like grease and motors can compromise cleanliness levels.

In contrast, cleanroom robots are meticulously designed to prevent dust generation, incorporating features such as magnetic fluid seals in sliding components. This ensures their compatibility with clean room environments, meeting class 100 or lower cleanliness standards (even reaching class 1 or lower depending on the specific product).

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Cyclone Separator

What Is a Cyclone Separator?

A cyclone separator is a device that separates particles mixed in a fluid.

It uses the difference between the density of the particles in the fluid and the density of the fluid itself to separate the particles in the fluid from the difference in centrifugal force generated by each. Pumps for pumping fluids containing solids or sand are expensive because the sealing parts must be crafted to prevent solids from entering.

Detection devices and other equipment may also be required. These problems can be solved by using a cyclone separator.

Uses of Cyclone Separators

Cyclone separators are used in a variety of industrial settings. The following are some examples of cyclone separator applications:

  • Removal of contaminants from exhaust gases
  • Collection of abrasive particles mixed with waste fluid after polishing
  • Classification and separation of fine particles
  • Removal of compounds from factory wastewater, wastewater treatment tanks, etc.
  • Recovery of crystals and raw materials generated in food, pharmaceutical, and chemical manufacturing processes
  • Removal of foreign matter from ultrasonic cleaning solutions and circulating cleaning solutions of high-pressure washers
  • Recovery of abrasive grains from blasting and water jetting
  • Removal of solids from sampling liquids
  • Widely used in industry as a pretreatment for accurate particle separation

Principle of Cyclone Separators

Cyclone separators are typically conical. Liquid mixed with particulate debris is poured into the cyclone separators from the pump discharge to generate a spiral flow.

Since there is a difference between the density of particulates in the fluid and the density of the fluid itself, there is also a difference in the centrifugal force generated by the spiral flow. The cyclone separators take advantage of this difference. Oil, water, and solids are knocked against the inner wall of the housing and fall along the wall.

The cleaned liquid is discharged from the top of the cyclone separator. The solids fall downward and are sent to the suction side of the pump for circulation.

Thus, cyclone separators are used for liquids containing a mixture of fine particles. However, even for liquids that do not contain a large amount of particulate debris, they may be used as a safety measure to prevent particulates from mixing.

Other Information on Cyclone Separators

1. Advantages and Disadvantages of Cyclone Separators

A cyclone separator is a device that separates foreign particles in a liquid or gaseous fluid and is not itself powered. Therefore, the advantages of cyclone separators are that they can be installed in a system that is already circulating and that they are low cost. Another advantage is that the main unit is maintenance free because it is a structure.

However, fine particles cannot be separated because they are carried by the fluid flow. The large pressure drop and the large energy required to maintain fluid speed are disadvantages.

2. Design of Cyclone Separator

Cyclone separators are designed according to the density of solids to be separated and the required separation rate. Among separators, cyclone separators are used for relatively high flow rates.

In addition, the capacity of cyclone separators is greatly affected by the capacity of the pump and blower, which are discharge devices. It is widely used as a dust collection system that requires little maintenance, but the important factor is the blower pressure.

If the airflow velocity is reduced by half, the dust collection capacity is greatly reduced, so the blower and pump pressure are the rate-limiting factors in the design of cyclone separators.

3. Bag Filters and Cyclone Separators

In the manufacturing process of powder products, cyclone separators are sometimes used in multiple stages of product classification and collection. In addition, a fabric filter may be combined with a bag filter in the latter stage.

Incinerators are also sometimes designed in combination when either of these single-stage facilities cannot meet regulatory limits. This is to compensate for the inability to collect fine particles, which is one of the drawbacks of cyclone separators.

However, one drawback of fabric filters is that they require periodic cleaning or replacement of the filter cloth. Combined with cyclone separators, the filter cloth replacement interval can be extended to reduce the load on the fabric filter. This reduces replacement work costs and running costs, such as disposal costs for replacement filter cloth.

When replacing the filter cloth, gas flow to the fabric filter must be stopped. Therefore, extending the filter cloth replacement interval extends the period of continuous operation, which is expected to improve productivity.

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Cleanroom Papers

What Is Cleanroom Paper?

Cleanroom paper, also known as dustproof or dust-free paper, is designed for use in cleanrooms.

It is characterized by its low dust emission, which is essential for cleanroom environments, and it also offers typical paper functions such as ease of copying, printing, and cutting.

Unlike standard copy paper and notebook paper, which emit dust particles and cannot be used in cleanrooms, most cleanroom papers are colored, often in blue or other distinctive colors, to differentiate them from regular papers.

Uses of Cleanroom Paper

Due to their low dust emission, cleanroom papers can replace regular copy paper and notebook paper in cleanrooms where dust generation is prohibited.

For instance, in semiconductor manufacturing plants, cleanroom papers are used for tables (flow charts) that detail work conditions and product types.

Some cleanroom papers are made with conductive fibers to provide conductivity. Electronic industrial products like silicon wafers and substrates are sensitive to static electricity during handling. Conductive cleanroom paper reduces the risk of static buildup and can be used as interleaving paper for such products. However, it should be tested when used as copy paper, as printing may not adhere well on certain types of copy machines.

Principle of Cleanroom Paper

Cleanroom papers are manufactured using different methods and materials compared to regular papers.

Ordinary copy paper and notebook paper are often made from short wood pulp fibers, which can shed easily and result in higher dust emissions. In contrast, cleanroom papers use long fibers that are tightly bonded to reduce dust emission.

Another distinction lies in the coloring process. Standard paper uses pigments such as calcium carbonate and titanium to achieve whiteness and opacity, which can generate dust. Cleanroom papers use liquid dyes as colorants, avoiding dust generation from pigments.

Additional measures to prevent dust emission include the use of resin to reinforce the fibers and prevent them from shedding.

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Rubber Hardness Tester

What Is a Rubber Hardness Tester?

A rubber hardness tester, as the name implies, is a device that measures the hardness of rubber.

Mainly, a measuring instrument called a durometer is used. This device measures the rubber hardness by the depth to which the needle is pushed into the sample when the sample is deformed by spring force.

Durometers can be classified into three types according to the hardness of the rubber to be measured: Type A, Type D, and Type E, which have different needle tip shapes. The hardness is determined by the force with which the needle is pressed against the sample and the area of the indentation.

Uses of Rubber Hardness Testers

Rubber hardness testers are used to evaluate the hardness of rubber. Specifically, they are used for car tires and erasers. In addition to rubber, it is also used to evaluate the hardness of elastomers and plastic products.

Principle of Rubber Hardness Testers

The most commonly used durometer for measuring hardness deforms a sample by pressing a needle against it under the force of a spring. At this time, the sample generates a repulsive force in response to the pressing force.

When both forces reach equilibrium, the amount by which the needle is pushed into the sample can be used to measure the hardness value. If the sample’s repulsive force is weak, the sample will be soft; if the repulsive force is strong, the sample will be hard.

Rubber Hardness Tester’s Information

1. How to Describe Hardness

The result of hardness measurement, not only for the durometer, is not a physical property value like weight and has no unit. It is the result of a certain method of testing, so it is necessary to describe the test method along with the numerical value. The measurement method and the notation of the results are defined in the standard.

The durometer type, indicated value, and time to reading are indicated in this way. (Omitted for measurements of 1 second or less.) Other standards use similar notation. It is important to check the notation method according to the intended test method.

The main standards that use the durometer are as follows:

  • ASTM D2240-2005
    Physical Properties of Rubber – Standard Test Method for Durometer Hardness
  • ISO 48-4
    Rubber-Hardness Test Method with Pocket Mold
  • ISO 868-2003
    Plastics – Durometer Test Method

2. Precautions for Measurement

When using the durometer, the following points should be noted.

  • If the sample rubber is affected by temperature or humidity, it cannot be measured accurately.
  • If the rubber hardness testers are pressed against the sample improperly, or if the surface of the sample is uneven or warped, accurate measurement will not be possible.
  • Repeatedly measuring the same spot on the sample will result in lower hardness, so when measuring multiple locations, please measure at different points. Generally, it is recommended to separate the measurement points by at least 6 mm.
  • Sample thickness also affects the measurement. Type A durometers require a thickness of 6 mm or more.
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Corner Cube

What Is a Corner Cube?

Corner Cubes are devices that retroreflect incident light back in the direction of incidence.

The reflected image is inverted. Unlike mirrors, which are retroreflective only at an angle of incidence of 0°, Corner Cubes’ retroreflectivity is effective even at large angles of incidence. This feature is frequently used for difficult optical-axis adjustment tasks or to reduce working time.

Corner Cube has three reflective surfaces. In general, the maximum allowable angle of incidence at which the phenomenon of total reflection of light can be obtained is theoretically limited to 5.7°.

Uses of Corner Cube

Corner Cubes are used as reflectors for laser-based length measuring machines. They were developed to measure the distance between the Moon and the Earth, and were placed on the lunar surface when the Apollo spacecraft landed on the Moon.

There are many things around us that use the same property. The red reflector on the back of a bicycle or the reflectors (orange or colorless) on the road or on the side of the road are made up of many very small reflectors. Recently, smaller sealed versions are also available, allowing Corner Cubes to be used in a wide variety of locations.

Corner Cubes mounted on vehicles and roads are often made of plastic, and highly accurate Corner Cubes can be used for surveying. Many cubes are made of glass, and their length can be measured from the time they return to the laser beam.

Corner Cube Principle

The three faces of a Corner Cube are placed in an orthogonal relationship to each other. The three planes are xy-plane, yz-plane, and zx-plane, respectively. For example, when light is reflected from the xy-plane, only the z-component of the 3-dimensional vector component indicating the direction of light travels has its sign reversed, while the x- and y-components remain unchanged. Similarly, the sign of the x component is reversed in the yz-plane and the sign of the y component is reversed in the zx-plane.

Due to this property, rays of light that are reflected sequentially in the three planes and whose incoming direction vector is [a, b, c] are [-a, -b, -c] when inverted. In other words, it returns light in the direction it came from. There are a total of six possible combinations of the order in which the incident light is inverted, determined by the position of the incident rays, resulting in the sign of all components being inverted regardless of the order in which they are reflected.

Types of Corner Cubes

Devices that reflect microwaves emitted from a radar in the direction of the radar antenna are called radar corner reflectors. Three conductive metal sheets or screens are pasted together at 90° to reflect incoming radio waves from the front in a parallel manner. However, the reflective surface must be larger than the incident wavelength to function.

Reversal mirrors are made by applying the Corner Cube principle. A reversal mirror is two mirrors combined at right angles. In a reversal mirror, the left and right sides of the image are reversed, but in a reversal mirror, the left and right sides are kept the same.

Corner Cube Structure

There are two types of Corner Cubes: hollow and prismatic. Both have the same basic structure that uses reflections on three surfaces.

Due to the “optical path difference” caused by the relative speeds of the observation station and the satellite, a slightly shifted orthogonality is more effective than a reflector with an exact orthogonality. Many of the reflectors actually used on satellites have their orthogonality intentionally shifted.

Corner Cube Reflector, Cube corners, and Corner reflector are other names for Corner Cube. Corner Cube Prisms and Corner Cube Mirrors are also called Corner Cube Prisms or Corner Cube Mirrors, depending on the reflection principle.