StudySmarter: Study help & AI tools
4.5 • +22k Ratings
More than 22 Million Downloads
Machine Design

Delve into the realm of Machine Design, a crucial domain within the field of Engineering. This article offers a comprehensive exploration of its meaning, history, and significance to engineering at large. Learn about key Machine Design principles, from balancing form and function to understanding the interplay between strength and rigidity. Discover real-life examples, the role of software, and the myriad applications of Machine Design across engineering fields. The introduction to Machine Design Standards should not be missed, probing into the necessity for strict adherence to maintain the quality of design.

Mockup Schule Mockup Schule

Explore our app and discover over 50 million learning materials for free.

Machine Design


Lerne mit deinen Freunden und bleibe auf dem richtigen Kurs mit deinen persönlichen Lernstatistiken

Jetzt kostenlos anmelden

Nie wieder prokastinieren mit unseren Lernerinnerungen.

Jetzt kostenlos anmelden

Delve into the realm of Machine Design, a crucial domain within the field of Engineering. This article offers a comprehensive exploration of its meaning, history, and significance to engineering at large. Learn about key Machine Design principles, from balancing form and function to understanding the interplay between strength and rigidity. Discover real-life examples, the role of software, and the myriad applications of Machine Design across engineering fields. The introduction to Machine Design Standards should not be missed, probing into the necessity for strict adherence to maintain the quality of design.

Understanding Machine Design

Machine Design is an essential branch of engineering that focuses on the creation of new and innovative machines and machine systems. This discipline applies principles of physics, material science and mathematics to conceive, analyse, design and manufacture mechanical systems. Having a well-rounded understanding of machine design is fundamental for any budding engineer wanting to make a mark in the industry.

Machine Design Meaning

In its core, machine design stands for the process of devising a machine, system or mechanism that serves a specific purpose or fulfils a predetermined function. This involves a comprehensive comprehension and application of various principles and laws of engineering.

Machine Design: It is the process of designing machine parts, systems or mechanisms, that will yield desired outputs, using principles and laws of engineering.

During the design process, factors such as functionality, cost-effectiveness, reliability, safety, aesthetics, and sustainability are taken into account. Fundamental concepts used in machine design include:
  • Mechanics
  • Kinematics
  • Thermodynamics
  • Materials Science
  • Structural analysis

History and Evolution of Machine Design

Throughout the course of history, machine design has undergone significant evolution. The industrial revolution paved the way for innovations in this field, with a shift from manual craftsmanship to mechanised manufacturing.

In the 18th century, engineers began to use graphical methods to represent the elements of a machine, the principles for which were refined in the 19th century through the development of descriptive geometry. At this time, gears, levers, and other machine components were drawn in their most general form, and then particular instances were derived by measurements from these general forms, an approach known as parametric design.

With technological advancements, the practice of machine design shifted from drawing boards to computer-aided design (CAD) systems.

For instance, to design a gear system today, engineers use software to build a 3D model of the machine, virtually inspect its functionality and then pass on the final design to manufacturing. This not only reduces errors but also significantly enhances efficiency.

Importance of Machine Design in Engineering

Machine design is a cornerstone of engineering. Understanding and implementing machine design principles are crucial due to reasons such as:
  • It streamlines manufacturing processes
  • Enhances machinery's efficiency and productivity
  • Ensures the safety, reliability and cost-effectiveness of machines
  • Serves as a creative outlet for engineers, allowing them to create innovative, effective solutions to complex problems
To elaborate, successful machine design ensures safe and effective machinery operation, thereby minimising the risk of accidents and breakdowns. Moreover, by bringing down the costs affiliated with manufacturing processes, machine design makes products more affordable for consumers while also increasing profitability for organisations. Finally, in this constantly evolving world, machine design provides the perfect platform for engineers to innovate and bring forth solutions that can help overcome challenges in various sectors including energy, healthcare, transportation and more.

Diving Deep into Machine Design Principles

Grasping the principles of machine design is akin to mastering the basics of a complex language. These principles are the alphabets which, when used correctly, help engineers communicate innovative designs. By understanding the core principles, you could craft a design that's not only functional but also cost-effective, safe, and sustainable.

Key Machine Design Principles

When you begin to study various Machine Design principles, few stand out as being fundamental building blocks for this field. These principles guide the process from start to finish and hold paramount significance in the world of Machine Design. They include:

  • The Balance between Form and Function
  • Understanding Strength and Rigidity
  • Material Selection
  • Fatigue and Fracture
  • Tolerance Stack Up
  • Kinematics and Dynamics Considerations

Balance Between Form and Function in Machine Design

The first principle, balance between form and function, is the crux of machine design. This principle asserts that the aesthetics and functionality of a machine or a mechanical system are equally important.

Form and Function: Form refers to the shape and structure, while Function refers to the purpose or role of a machine part or mechanism.

The aim here is to maintain an ideal balance, ensuring the machine is visually appealing while also serving its purpose effectively. Design engineers need to consider various design parameters, dimensions, and constraints to ensure the final product is both efficient and aesthetic.

For instance, consider a race car. A lot of attention is given to the aesthetics of the car, its streamlined form to be precise. However, no compromises are made on its function which is speed and performance. The car's design, therefore, is the perfect marriage of form and function.

Understanding Strength and Rigidity in Machine Design Principles

Fundamental to any machine design is the concept of strength and rigidity. Strength is the property of a material to resist forces without breaking or yielding, while rigidity is the capability of a part or material to resist deformation when subjected to stress.

Strength: The ability of a material or component to withstand applied forces without failing in functionality. Rigidity: The property of a structure that measures its resistance to deformation in response to an applied force.

Engineers need to assess the forces and stresses that a machine or part will experience in its lifecycle and then choose materials and design shapes to ensure the component can endure these forces. This important principle impacts the reliability, performance, and lifespan of a machine.

The design strength of a machine component is often calculated using the formula: \( \text{Strength} = \frac{\text{Load}}{\text{Area}} \). Hence, in order to increase the strength of a structure, either the load acting on it should be decreased or the area over which it is distributed should be increased.

In-depth knowledge of materials science and structural mechanics are prerequisites to successfully implementing this principle. Advances in material science often lead to the development of stronger, more rigid and lighter materials, thereby furthering the capabilities of machine design.

A good example is how airplane manufacturers often use titanium alloys for critical parts because of their high strength-to-weight ratio and excellent temperature resistance. This understanding of an alloy's strength and rigidity increases the reliability and safety of the aircraft, while also enhancing fuel efficiency by reducing weight.

Thus, proficient understanding and application of these principles could elevate you from a novice to a master in the art of machine design.

Intriguing Examples of Machine Design

Machine design is an ever-pervasive field, the impact of which could be seen in almost all aspects of life. From the simple lever being used to lift weights to intricate robotic arms used in modern manufacturing, machine design plays a pivotal role. Let's delve deep into some intriguing instances of machine design which you encounter in everyday life and in industrial settings.

Machine Design Examples in Everyday Life

Not all examples of machine design are complicated machines used in industries or research. Some of the most remarkable examples are common items we interact with daily.

The first compelling example of machine design in our everyday life is the bicycle. It's an elegant design using simple machines that amplify human power. The pedals and its crankset make use of lever principles, while the chain and sprocket setup is a clear example of a gear train. These components, when assembled together, allow the bicycle to multiply the rider's effort and travel at fast speeds with lesser exertion.

Bicycle: A simple vehicle with two wheels in tandem, a seat, handlebars for steering, and pedals by which it is propelled. Bicycle design is a significant example of applied physics and engineering principles.

The second noteworthy example is the sewing machine. It makes use of a complex cam system to synchronise needle movement with the shuttle carrying the thread. The needle pierces the fabric to create a loop, and the shuttle passes through this loop to create a lock stitch.
Bicycle Gear trains and lever principles
Sewing Machine Cam mechanism for synchronising needle and shuttle
Finally, one cannot ignore the impact of machine design on our communication – the telephone. The telephone's functioning includes an intricate combination of electrical circuits and mechanical systems. The receiver converts the analog sound signals into electrical impulses, which are transmitted via cables, and then reconverted back to sound signals at the recipient’s end.

The complex function of telephones, from analog ones to modern smartphones, is a product of intricate machine design, combining principles from electrical engineering and telecommunications.

The examples above illustrate that even things that seem simple can represent sophisticated machine design applications.

Industrial Machine Design Examples

Industrial environments yield a fascinating range of machine design examples. In these settings, machine design principles are leveraged to increase efficiency, automate processes, and improve safety. Among these, a prominent machine that deserves attention is the hydraulic press. This device utilises Pascal’s law – a principle of fluid mechanics – to amplify force. It is used for tasks requiring substantial force such as forming metal parts, moulding plastic, or crushing objects.

Hydraulic Press: A machine using hydraulic cylinder to generate a compressive force, based on Pascal's principle of pressure throughout a closed system being constant.

Next up, there is the CNC machine. Also known as Computer Numerical Control machines, they make use of intricate software programming and motor control systems to cut and shape materials with high precision and consistency. The assembly line robotic arm is another interesting instance. These often complex mechanisms are designed to mimic the human arm's range of motion, affording flexibility in manipulating objects on an assembly line. They can be fitted with different 'end-effector' tools, making them versatile helpers in production processes.
Hydraulic Press Based on Pascal’s Principle
CNC Machine Software Programming and Motor Control Systems
Assembly Line Robotic Arm Mimics range of motion of human arm

The flexibility and programmability of assembly line robotic arms allow factories to quickly transition between different products without needing to build dedicated assembly machinery for each, increasing efficiency and reducing downtime.

Taking a closer look at these examples enlightens us about how the principles of Machine Design are put into action to answer specific industry needs, supporting the economy and our modern way of life.

The Role of Software in Machine Design

The age of digital transformation has dawned upon the engineering sector, bringing a radical shift in the way machine design is approached and implemented. The introduction and evolution of machine design software have brought an end to the tedious process of manual designing. The role of software in machine design is instrumental, making the entire procedure more accurate, efficient, and time-saving. This shift doesn't only enhance the design process but also complements other aspects of production, project management, simulation, and testing. Today's software solutions are thus intensely interwoven with all facets of the engineering process.

Overview of Machine Design Software

Let's get a broad perspective on Machine Design Software. These software solutions are computer programs that aid engineers during the design phase of creating new machines or improving existing ones. They provide a suite of robust tools to sketch, model, simulate, and test new product designs. And it's not just about design; these advanced software solutions also assist in cost estimation and lifecycle management of the product.

A diverse range of software solutions cater to various facets of machine design. Some address specific tasks like CAD (Computer-Aided Design) software for 3D modelling, CAE (Computer-Aided Engineering) software for simulation and validation, whereas others like PLM (Product Lifecycle Management) software offer a comprehensive solution that covers the product's entire lifecycle, from inception to disposal.

Some well-regarded machine design software solutions encompass:

  • Autodesk AutoCAD
  • SolidWorks
  • PTC Creo
  • Siemens NX
Each software brings unique capabilities to the table, catering to different industrial needs. In comparison, some offer superior 3D modelling tools, while others excel in simulation and dynamics. Hence, the choice of software often depends on the specific requirements of the project at hand.

It's noteworthy that these software tools are not just limited to sketching and drawing but also extend to simulation and analysis. For instance, you can simulate real-world conditions and examine how your design would perform under such circumstances, thanks to the Finite Element Analysis (FEA) capabilities some of these software solutions offer. By predicting machine response, you can nip potential performance or safety issues in the bud.

By offering these extensive capabilities, Machine Design Software is effectively bridging the gap between theoretical engineering concepts and practical application, thereby enabling design engineers to create efficient, reliable, and robust mechanical systems.

How Machine Design Software Facilitates Engineering Tasks

One of the paramount ways machine design software assists engineering tasks is through 3D modelling. With software tools, you can create a 3D model of the machine, offering a realistic and comprehensive representation of the design. It allows a detailed visual analysis that can help spot design issues and inconsistencies that might potentially be overlooked on 2D drawings.

Besides visualisation, it also extends greater control over design parameters. Let's look at the example of Autodesk Fusion 360 software. Here is a sample script to change the radius of a circle:

parameters = design.allParameters
radiusParam = parameters.itemByName('BaseCircleD1')
radiusParam.expression = '25 mm'

This sample scripts' output is changing the parameter 'BaseCircleD1' within the 3D model to 25 mm. This level of detail would be near impossible to access manually. The 3D modelling software offers the flexibility to tweak different parameters of design until an optimal configuration is achieved.

Next up, the simulation capability within machine design software is a game changer. Simulation makes it easier to predict how the design will perform under real-world conditions. Finite Element Analysis (FEA) is often used to assess the machine under different loading conditions. The equation employed in the FEA is as follows:

\[ F = k \cdot u \] where \( F \) is the force, \( k \) is the stiffness matrix, and \( u \) is the displacement vector. Feeding the equations into the software helps assess the displacement under different applied forces, making it possible to analyse and foresee potential points of failure.

Lastly, machine design software also contributes enormously to the documentation process. The software automatically generates technical drawings, assembly instructions, and bills of materials (BOM), a task which if manually done, could prove time-consuming and error-prone. Also, as these documents are linked to the design, any changes in the design are automatically reflected in the documentation, ensuring all documents are always up to date.

In conclusion, machine design software facilitates engineering tasks by enhancing visualisation through 3D modelling, bringing predictability through simulation, and easing documentation. By these, they save time, improve efficiency, and increase the reliability of machine design processes.

Exploring Machine Design Applications

Machine Design, the indispensable pillar of engineering, extends its applications across a myriad of industries. The process of devising new or improved mechanical systems has always been at the forefront of technological advancements, driving many innovations, and paving the way for the evolution of multiple sectors. With countless practical applications permeating various engineering fields, let's delve deeper to understand exactly how machine design is making a difference.

Practical Machine Design Applications

The practical applications of machine design cover not just the creation of new machinery but also enhancing existing systems. It's interesting to note how engineers exploit machine design principles to drive productivity, efficiency, and safety across an array of ventures.

Manufacturing is one such industry driven by machine design. Engineers design devices and tools to enable automated production lines, reducing manual labour, time, and error. The designs encompass simple manual tools to intricate, computer-controlled manufacturing units. Moreover, the role of machine design extends to maintaining and improving the efficiency of existing lines, thereby enhancing productivity.

Machine design also significantly impacts the automotive industry. Be it the design of engines, gear systems, suspensions, or braking systems, machine design principles are at play. The design of these components not only determines the efficiency and safety of the vehicle but also extends to the comfort and convenience of the driver and passengers. An exemplary display of machine design application in this industry is the design of anti-lock braking systems (ABS).

Another key area influenced by machine design is the energy sector. Design engineers specialise in constructing turbines, generators, solar panels, and other equipment involved in harnessing and generating power. The efficiency, reliability, and sustainability of these devices significantly depend upon effective machine design.

Also, when you think robotics, think machine design. Solar-powered robots, robotic arms in manufacturing, drones for rescue missions, or robots for surgical procedures - it's machine design that brings these applications to life.

Here are the applications summed up:

  • Manufacturing
  • Automotive
  • Energy
  • Robotics

Calling out one application of machine design within

the manufacturing sector

, consider the design of a CNC (Computer Numerical Control) machine. These automated, highly-precise machines, comprising motors, drive systems, slides, and the control unit perform operations like drilling, turning, or milling. The controller, designed by software such as G-code, breaks down the operations into tiny steps. Consider the following G-code programming example to instruct CNC operations:
N10 G21 
N20 G90 
N30 G00 X0 Y0 
N40 M03 S1200
N50 G01 X45 F250 
N60 G02 X60 Y15 I0 J15 F100 
N70 G01 Y30 F250 
N80 G00 X120 
N90 M05 
N100 G00 X0 Y0 
N110 M30

The G-code operates the CNC machine by managing movements, tool speed, feed rate, and coolant application. The intricacies involved in a CNC machine’s design showcase the practical implications of machine design in the manufacturing sector.

Machine Design Applications in Various Engineering Fields

Any field of engineering that involves the design, construction, and usage of machines is directly influenced by machine design. Starting with mechanical engineering, machine design serves as a cornerstone, dictating the design and development of all mechanical entities. However, its relevance spans out to other engineering areas too.

In civil engineering, machine design principles aid the creation of heavy machinery used for construction, like cranes and facilitated shovels or excavators. These machines are essential for construction processes and are carefully tailored to execute specific tasks while ensuring maximum operator safety.

For electrical engineers, machine design concerns the creation of electric tools and apparatus. For instance, the design of motors, generators, transformers, or circuit components oblige strict adherence to machine design principles to ascertain optimal performance and safety.

Similarly, machine design plays a crucial role in aeronautical engineering as well. The development of aircraft engines, hydraulic systems, or flight control mechanisms deeply rely on competent machine design.

Let's look at a practical example of machine design application in civil engineering with

the design of a crane.

. A crane is a machine equipped with a hoist, wire ropes, and sheaves that can be used to lift and lower heavy materials and to move them horizontally. The efficiency and functioning of the crane are intricately linked with its design.

Consider the load L that a crane must lift. The design of the crane must ensure that the sum of the moments around any point equals zero. Therefore, the equation for the balance of moments is as follows:

\[ L\times d = M_{cg} \] where \( L \) is the load, \( d \) is the distance from the load to the balance point, and \( M_{cg}\) is the moment produced by the weight of the crane about the balance point.

Here is how different engineering domains are driven by machine design:

  • Mechanical Engineering
  • Civil Engineering
  • Electrical Engineering
  • Aeronautical Engineering

With such wide-ranging applications across various engineering fields, the importance and influence of machine design principles are undeniable. Through constant design improvements and innovation, machine design continues to refine and reshape numerous sectors, enhancing productivity, safety, and efficiency on a grand scale.

Importance of Adherence to Machine Design Standards

Adherence to machine design standards is paramount for novice and seasoned design engineers alike. By considering these constructed guidelines during planning and execution, professionals can ensure that the output is consistent, efficient, and in compliance with safety measures.

An Introduction to Machine Design Standards

Machine Design Standards, defined by recognised authorities like ISO (International Organisation for Standardisation), are rules and recommendations created to direct the design, production, and utilisation of machines. These standards form a fundamental basis for ensuring uniformity, quality, safety, and efficiency in machine design.

Standards are both guidelines and law in the engineering environment. Moreover, their adherence is key for design engineers to make informed decisions and navigate pitfalls of unsafe or inefficient design. To ensure the effectiveness of the equipment created, standards cover a wide spectrum of machine aspects.

These aspects include:

  • Design criteria
  • Materials selection
  • Manufacturing methods
  • Inspection and testing regulations
  • Operational procedures

A primary feature of these standards concerns the machine’s functional safety. They aid the designer in defining the machine's lifecycle in terms of safety from design, assembly, installation, maintenance to decommissioning stages. For instance, ISO 13849 and IEC 62061 provide rules for control systems ensuring the safety of machinery.

These standards also lay down directives for safeguarding measures - the design and implementation of protective measures such as physical barriers or light curtains. For instance, ISO 14119 specifies principles for the design and application of interlocking devices associated with guards. Following these standards can curb human-machine interaction related accidents and foster safer working environments.

    vertical:Safety gate,
    non-vertical:Light curtains
  Interlocking devices: {
    Coded:RFID cards

This code beautifully summarises safety measures such as guarding and interlocking devices, suggesting how each has a role in machine safety.

The Impact of Machine Design Standards on the Quality of Design

Machine Design Standards significantly influence the quality of design, asserting their importance in various dimensions. The most prominent one being - fostering design uniformity. Standards offer a reference framework that ensures a uniform approach in design, facilitating interchangeability of machine components. They also aid in simplifying the design, leading to economic production of quality machines.

An integral part of these standards is directed towards guaranteeing functional safety. They advocate the use of safety components and guidelines for safe control systems, leading to the creation of safe and reliable machines.

A good focus is also on ensuring sustainability. Aspects concerning material selection, efficient energy usage, and directives for reduced environmental impact make the designs eco-friendly.

Machine design standards can influence the quality of design in the following ways:

  Design Uniformity -> realize interchangability,
  Functional Safety -> ensure reliable machines,
  Sustainability -> make the design ecofriendly

Consider an example where neglecting design standards can cause failure.

Assume a centrifugal pump designed without following standards concerning impeller design and material selection.

Such a pump would likely encounter problems like cavitation or corrosion, leading to its premature failure. Cavitation, occurring when the pump suction is under low pressure, can be kept in check using the formula: \[ NPSH = P_{atm} - P_{vapor} \]

Where \(NPSH\) is the Net Positive Suction Head, \(P_{atm}\) is the atmospheric pressure, \(P_{vapor}\) is the vapour pressure of the liquid. By not maintaining a sufficient \(NPSH\) as per standards, the pump will suffer cavitation, damaging its components.

Hence, the design governed by necessary standards enhances product reliability, significantly reducing the risk of failure and extending the product's life. An enduring product positively impacts customer satisfaction and trust.

Lastly, standards provided by the ISO concerning product documentation and quality assurance play a crucial role in making the design transparent and traceable. Detailed design and quality documentation make it easy to monitor and trace any discrepancies, thus contributing to overall quality control.

The adherence to machine design standards profoundly affects the quality of machine design, highlighting the magnified role they undertake in different aspects of machine creation. Therefore, understanding and following these guidelines is imperative for any design engineer to create top-notch and safe machinery.

Machine Design - Key takeaways

  • Machine Design is an essential part of engineering and is used to devise new or improved mechanical systems, with applications across a myriad of industries.
  • Some common examples of machine design include everyday appliances like the bicycle and the sewing machine, while industrial examples include hydraulic presses, CNC machines, and assembly line robotic arms.
  • Software plays an instrumental role in machine design, aiding in sketching, modeling, simulating, testing, and lifecycle management of various designs. Examples of such software include Autodesk AutoCAD, SolidWorks, CATIA, and Siemens NX.
  • Alongside visualisation and analysis, machine design software also provides documentation assistance, generating technical drawings, assembly instructions, and bills of materials (BOM), thereby reducing human error and saving time.
  • Practical applications of machine design principles span across sectors such as manufacturing, automotive, energy, and robotics, contributing to productivity, efficiency, and safety in these fields.

Frequently Asked Questions about Machine Design

Machine design is a branch of engineering that focuses on creating new or improving existing machines. It entails understanding the operational requirements, conceptualising and planning the machine structure, and ultimately creating detailed designs and schematics.

Designing a machine involves several stages: identifying the requirement, conceptualising and evaluating the design, detailed drawing and analysis, material selection, manufacturing the prototype, and final testing and implementation. The process also requires good knowledge of mechanical principles, safety considerations, and cost-effectiveness.

Examples of machine design include the design of gears, bearings, clutches, brakes, and levers. It also involves designing machinery like engines, turbines, air conditioning systems and heavy machinery used in industries. Even the development of everyday objects like kitchen appliances and power tools involves machine design.

The principles of machine design include: understanding the requirements and purpose of the machine; selecting the right materials for its components; ensuring safety, reliability and durability; efficient energy consumption; and designing for ease of production, operation, maintenance, and cost-effectiveness.

The principal standards that govern machine design include the International Organization for Standardization (ISO), the British Standards Institution (BSI), and the American Society of Mechanical Engineers (ASME). They provide guidelines on safety, reliability, efficiency, and interoperability of machine designs.

Test your knowledge with multiple choice flashcards

What is machine design and what principles does it apply?

What is the importance of machine design in engineering?

What does the principle of balance between form and function in machine design involve?


What is machine design and what principles does it apply?

Machine design is the process of creating new and innovative machines and systems. It applies principles of physics, material science, and mathematics to conceive, analyse, design, and manufacture mechanical systems for a predetermined function or purpose.

What is the importance of machine design in engineering?

Machine design streamlines manufacturing processes, increases machinery's efficiency and productivity, ensures safety and cost-effectiveness of machines, and is a creative outlet for engineers to devise solutions to complex problems.

What does the principle of balance between form and function in machine design involve?

This principle asserts that the aesthetics (form) and functionality (function) of a machine or a mechanical system are equally important. The goal is to create a machine that is visually appealing while effectively serving its purpose.

What do the terms 'strength' and 'rigidity' refer to in the principles of machine design?

Strength is the property of a material to resist forces without breaking or yielding, while rigidity is the capacity of a part or material to resist deformation when subjected to stress.

What are some examples of machine design in everyday life and how do they work?

Some examples include a bicycle which uses gear trains and lever principles, a sewing machine that uses a complex cam mechanism to synchronize the needle and shuttle movement, and a telephone that combines electrical circuits and mechanical systems to convert sound signals into electrical impulses and vice versa.

What are some examples of industrial machine design and how do they work?

Examples include a hydraulic press that uses Pascal’s Principle to amplify force, a CNC machine which uses software programming and motor control systems for precision, and an assembly line robotic arm that mimics the range of human arm motion.

Join over 22 million students in learning with our StudySmarter App

The first learning app that truly has everything you need to ace your exams in one place

  • Flashcards & Quizzes
  • AI Study Assistant
  • Study Planner
  • Mock-Exams
  • Smart Note-Taking
Join over 22 million students in learning with our StudySmarter App Join over 22 million students in learning with our StudySmarter App

Sign up to highlight and take notes. It’s 100% free.

Start learning with StudySmarter, the only learning app you need.

Sign up now for free

Entdecke Lernmaterial in der StudySmarter-App