Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

Graphical Linkage Synthesis

Lecture

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

3.1: Synthesis

Definition: 1. Putting together2. Creating something new

You cannot analyze anything until it has been synthesized into existence

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

Synthesis in Kinematics

Qualitative SynthesisUsed when no mathematical technique exists.Sometimes requires “design by successive analysis”

Assume a possible solutionAnalyze it to determine suitabilityRevise solution based on insights gained in the analysis

Type SynthesisWhat type of device do I need for the task?

Linkage?, Cam?, Gears?, Air cylinders?, Other? A Combination?Quantitative Synthesis

Used when a mathematical technique exists to directly create a solution. (Only for certain classes of problems)

Dimensional Synthesis

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

3.2: Function, Path and Motion Generation of (Linkage Synthesis)

Three TypesFunction Generation

Output motion is a defined mathematical function of the input motion, e.g., x = r cos(q).

Path GenerationOutput motion is a defined path along a set of x,y points.

Motion GenerationOutput motion is a set of positions of a line defined as x, y, q successive locations.

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

Function Generator

Scotch Yoke Mechanism x = r cos(θ)

Function Generation- Output motion is a defined mathematical function of the input motion, e.g., x = r

cos(q).

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

Path Generator

Film Advance Mechanism

Path GenerationOutput motion is a defined path along a set of x,ypoints.

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

Motion Generator

Three Positions of a Line

Motion GenerationOutput motion is a set of positions of a line defined as x, y, q successive locations

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

3.3: Limiting Conditions

Degree of freedom (number of inputs?)Grashof condition (rotation required?)Transmission anglesPresence of toggle positions

May be either desirable or undesirable

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

3.3.1:Toggle Positions Limit Motion

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

3.3.2: Transmission Angle

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

3.4: Dimensional Synthesis

Determines the proper link lengths of a mechanism to perform the required task.

Applicable to all three modalities: path, motion, or function synthesis.Can be done either graphically or analytically.One method can be used to check the other.

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

3.4.1Two-Position Synthesis - Construction

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

3.4.1: Two-Position Synthesis - Results

Check:Grashof ConditionTransmission Angles

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

3.4.2: A Three-Position Mechanism

Simulation

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

3.4.2:Three-Position Synthesis - Construction

A1

B1

A2B2

A3B3

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

3.4.2:Three-Position Synthesis - Results

A1

B1

A2B2

A3

B3

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

3.4.2:Three-Position Synthesis – Adding a Driver Dyad

A1

B1

A2B2

A3

B3

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

3.4.3: 3 Positions with Specifying Fixed Pivots

Previous method allowed fixed pivots to “come out in the wash.”Often, we have limits on possible locations of fixed pivots.Examples 3-7 and 3-8 show a graphical method to choose the fixed pivots and synthesize a suitable 3-position linkage.

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

3.4.3: More Than 3 Positions?

The more constraints we have the more complicated the problem.Difficult to solve graphically.Use quantitative synthesis.Requires computer.Designer will need to make some free choices of variable values

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

3.5 Quick-Return Mechanisms

Many machine design applications have a need for a difference in average velocity between their FORWARD and RETURN stroke.

•Forward stroke – External work being done

•Return stroke – accomplish as rapid as possible

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

3.5.2:Quick-Return Fourbar Linkage

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

3.5.3: Quick-Return Sixbar

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

Crank-Shaper Quick Return (Simulation)

Graphical Linkage Synthesis3.1: SynthesisSynthesis in Kinematics 3.2: Function, Path and Motion Generation of (Linkage Synthesis)Function GeneratorPath GeneratorMotion Generator3.3: Limiting Conditions3.3.1:Toggle Positions Limit Motion3.3.2: Transmission Angle3.4: Dimensional Synthesis3.4.1Two-Position Synthesis - Construction3.4.1: Two-Position Synthesis - Results3.4.2: A Three-Position Mechanism3.4.2:Three-Position Synthesis - Construction3.4.2:Three-Position Synthesis - Results3.4.2:Three-Position Synthesis – Adding a Driver Dyad3.4.3: 3 Positions with Specifying Fixed Pivots3.4.3: More Than 3 Positions?3.5 Quick-Return Mechanisms3.5.2:Quick-Return Fourbar Linkage3.5.3: Quick-Return SixbarCrank-Shaper Quick Return (Simulation)