Synthesis of Mechanism

Contents

Recall synthesis of mechanism 1

Recall classification of synthesis problem 2

Recall synthesis of function generation: a. Precision point b. Structural error 3

Recall the Freudenstein’s equation 4

Recall the graphical synthesis of four bar mechanism 5

Recall the graphical synthesis of single slider crank mechanism 6

Recall synthesis of mechanism

In mechanical engineering, synthesis of mechanisms refers to the process of designing and creating a mechanism to achieve a specific function or task. The process typically involves identifying the desired motion or output of the mechanism and then designing the individual parts or components that will work together to produce that motion.

The synthesis of mechanisms typically involves several stages, including:

1. Analysis of the desired motion or output: This involves identifying the specific motion or output that the mechanism needs to produce. This may involve analysing the input and output forces and torques, as well as the kinematics of the system.
2. Design of individual components: Once the desired motion or output has been identified, the individual components of the mechanism can be designed. This may involve designing linkages, gears, cams, and other parts to work together to produce the desired motion.
3. Assembly and testing: Once the individual components have been designed, they can be assembled into the final mechanism. The mechanism can then be tested to ensure that it is functioning properly and producing the desired motion.
4. Optimization: If necessary, the mechanism can be optimised to improve its performance. This may involve making adjustments to individual components, or redesigning the mechanism as a whole to achieve better performance.

Overall, the synthesis of mechanisms is an important part of mechanical engineering, and it plays a critical role in the design and development of many types of machines and systems. By carefully designing and testing the individual components of a mechanism, engineers can create machines that are both effective and efficient, and that can perform a wide range of tasks and functions.

Recall classification of synthesis problem

In mechanical engineering, the synthesis problem refers to the task of designing a mechanism to perform a specific function or motion. The synthesis problem can be classified into several different types, based on the specific constraints and requirements of the design problem. Some of the most common types of synthesis problems include:

1. Motion generation: This type of synthesis problem involves designing a mechanism to produce a specific motion or path, such as a straight line, circular motion, or other types of motion.
2. Function generation: This type of synthesis problem involves designing a mechanism to perform a specific function, such as lifting, rotating, or linear motion.
3. Path generation: This type of synthesis problem involves designing a mechanism to move along a specific path or trajectory, such as a straight line, a curve, or a complex motion path.
4. Optimal design: This type of synthesis problem involves designing a mechanism that maximises or minimises a specific performance metric, such as minimising the weight or size of the mechanism, or maximising its efficiency or strength.
5. Kinematic synthesis: This type of synthesis problem involves designing a mechanism to satisfy a specific set of kinematic constraints, such as maintaining a constant velocity or acceleration.
6. Dynamic synthesis: This type of synthesis problem involves designing a mechanism to satisfy a specific set of dynamic constraints, such as minimising vibration or shock.

Overall, the classification of synthesis problems helps engineers to better understand the specific requirements and constraints of a design problem, and to develop effective solutions that meet those requirements. By carefully analyzing the specific constraints and requirements of a design problem, engineers can develop innovative and effective mechanisms that are both functional and efficient.

Recall synthesis of function generation: a. Precision point b. Structural error

Function generation is a type of synthesis problem in mechanical engineering that involves designing a mechanism to perform a specific function, such as lifting, rotating, or linear motion. Within the category of function generation, there are two important concepts that are often considered during the design process: precision point and structural error.

1. Precision point: In the context of function generation, a precision point refers to a specific location or position that the mechanism must achieve with a high degree of accuracy. For example, in a robotic arm, a precision point might be the location where a tool must be accurately positioned for a specific task. Achieving a precision point requires careful design and engineering of the mechanism, taking into account factors such as dimensional tolerances, friction, and other sources of error.
2. Structural error: Structural error refers to errors in the design or construction of the mechanism that can cause deviations from the intended function or motion. These errors can be caused by factors such as dimensional tolerances, material properties, or other sources of variation. Structural error can be particularly problematic in function generation mechanisms, where even small errors can cause significant deviations from the intended function. To minimize structural error, engineers must carefully design and construct the mechanism, taking into account factors such as manufacturing tolerances and material properties, and perform careful testing and validation to ensure that the mechanism is functioning as intended.

Overall, the synthesis of function generation mechanisms involves careful consideration of factors such as precision points and structural error, as well as a wide range of other factors such as kinematics, dynamics, and performance requirements. By carefully designing and testing the mechanism, engineers can develop mechanisms that are both functional and efficient, and that can perform a wide range of tasks and functions.

Recall the Freudenstein’s equation

Freudenstein’s equation is an important mathematical equation used in the design and analysis of four-bar linkages, which are a common type of mechanical mechanism used for transmitting motion and force. The equation was first developed by J. Freudenstein in the 1950s and is used to determine the number of solutions for a given four-bar linkage, as well as the values of the input and output angles for each solution.

The equation takes the form:

f + g + h + j = 0

where f, g, h, and j are functions of the four bar linkage parameters, including the lengths of the bars and the angles between them. The equation is a polynomial of degree six in the cosine of the output angle, and can be used to determine the maximum and minimum values of the output angle for a given input angle.

Freudenstein’s equation is particularly useful in the design and analysis of mechanical systems, as it provides a way to determine the possible configurations of a given mechanism and to optimize the performance of the mechanism for a specific task. By analyzing the possible solutions provided by the equation, engineers can develop mechanical systems that are both efficient and effective, and that can perform a wide range of tasks and functions.

Recall the graphical synthesis of four bar mechanism

The graphical synthesis of four-bar mechanisms is a process used to design a four-bar mechanism to achieve a specific motion or function. The synthesis involves using a graphical method to determine the necessary link lengths and angular positions of the mechanism.

The graphical synthesis of four-bar mechanisms typically involves the following steps:

1. Specify the input and output motion: The first step is to define the desired input and output motion of the mechanism. This could be a specific path or motion of the output link, or a specific angular relationship between the input and output links.
2. Construct a velocity polygon: A velocity polygon is a geometric construction that represents the velocities of the various links in the mechanism. It is constructed by drawing lines to represent the angular velocities of each link, and then closing the polygon. The velocity polygon can be used to determine the necessary link lengths and angular positions to achieve the desired motion.
3. Construct a position polygon: A position polygon is a similar construction that represents the angular positions of the links in the mechanism. It is used to determine the exact positions of the links at various points in the motion.
4. Determine link lengths and angular positions: Using the velocity and position polygons, it is possible to determine the necessary link lengths and angular positions to achieve the desired motion or function.
5. Refine the design: Once the initial link lengths and angular positions have been determined, the design can be refined to optimize the performance of the mechanism for the specific application.

The graphical synthesis of four-bar mechanisms is a powerful tool for mechanical engineers and designers, as it provides a way to create complex mechanical systems that can perform a wide range of functions with precision and accuracy.

Recall the graphical synthesis of single slider crank mechanism

The graphical synthesis of a single slider-crank mechanism is a process used to design a mechanism that can convert rotary motion into reciprocating motion or vice versa. The mechanism is made up of four links, one of which is fixed, and one that slides back and forth along the fixed link.

The graphical synthesis of a single slider-crank mechanism typically involves the following steps:

1. Define the input and output motion: The first step is to define the desired input and output motion of the mechanism. This could be a specific path or motion of the slider or crank, or a specific angular relationship between the input and output links.
2. Construct a velocity polygon: A velocity polygon is a geometric construction that represents the velocities of the various links in the mechanism. It is constructed by drawing lines to represent the angular velocities of each link, and then closing the polygon. The velocity polygon can be used to determine the necessary link lengths and angular positions to achieve the desired motion.
3. Construct a position polygon: A position polygon is a similar construction that represents the angular positions of the links in the mechanism. It is used to determine the exact positions of the links at various points in the motion.
4. Determine link lengths and angular positions: Using the velocity and position polygons, it is possible to determine the necessary link lengths and angular positions to achieve the desired motion or function.
5. Refine the design: Once the initial link lengths and angular positions have been determined, the design can be refined to optimize the performance of the mechanism for the specific application.

The graphical synthesis of a single slider-crank mechanism is a powerful tool for mechanical engineers and designers, as it provides a way to create complex mechanical systems that can perform a wide range of functions with precision and accuracy. The mechanism is widely used in many industrial applications, including internal combustion engines, pumps, and compressors.