## Problem Statement

Find the velocity vectors of points B and C at given position when w2 is 150 revolutions per minute CCW. The dimensions are given in mm.

Use analytical (vector loop) method.

a) Derivation of equations using vector loop

b) Calculation of slip velocity at slider block, θ3, ω3

c) Calculation of vectors VB and VC in Cartesian form

SW portion (15 points): Build models in SolidWorks and solve it using Motion a) (4 points) 4 parts b) (2 points) Assembly c) (3 points) Motion Study d) (2 points) 2 Excel graphs of velocity for point B and C e) (4 points) Velocity vectors of points B and C in Cartesian form

Paper portion (15 points): Use analytical (vector loop) method. a) (5 points) Derivation of equations using vector loop b) (5 points) Calculation of slip velocity at slider block, θ3, ω3 c) (5 points) Calculation of vectors VB and VC in Cartesian form

#### 2) Assume that the angular velocity, w2 is 100 revolutions per minute CCW. Find the velocity vectors at B, C, and D at given position. The dimensions are in inches.

SW portion (15 points):

Build models in SolidWorks and solve it using Motion Analysis

a) (3 points) 4 parts

b) (3 points) Assembly

c) (3 points) Motion Study

d) (3 points) 3 Excel graphs of velocity in magnitude for points B, C, and D

e) (3 points) Velocity of points B, C and D in magnitude

Paper portion (15 points):

Use instant center method.

a) (3 points) Sketch (annotate) the instant center points

b) (3 points) Calculation of VB

c) (3 points) Calculation of ω3

d) (3 points) Calculation of VC

e) (3 points) Calculation of VD

#### 3) Find the velocity vectors of points C and D at given position when VB is 6.1 mm/second. The dimensions are given in mm.

SW portion (15 points):

Build models in SolidWorks and solve it using Motion

a) (3 points) 3 parts

b) (2 points) Assembly

c) (3 points) Motion Study (Using linear motor)

d) (2 points) 2 Excel graphs of velocity

e) (5 points) Velocity vectors of points C and D in Cartesian form

Paper portion (25 points):

a) (10 points) Use instant center method.

(4 points) Sketch (annotate) the instant center points

(3 points) Calculation of VC

(3 points) Calculation of VD

b) (15 points) Use analytical method.

(7 points) Derivation of equations using vector loop

(4 points) Calculation of slip velocity at slider C, and angular velocity of the triangle

(4 points) Calculation of vectors VC and VD in Cartesian form.

## Solution

We have Solved these problems very carefully and step by step using SolidWorks and on Paper by using the methods described above. If you need any Solution the contact us. Below is the just guide

## 1. Introduction to Crank Slider Mechanism

A crank slider mechanism is a mechanical system commonly used to convert rotational motion into linear motion or vice versa. It comprises a rotating crank, a connecting rod, and a sliding block. This mechanism is foundational in various machines, such as internal combustion engines, pumps, and compressors.

## 2. Understanding Velocity Analysis

Velocity analysis is the process of evaluating the velocities of different components in a mechanism to understand their motion characteristics. This analysis is crucial for predicting the dynamic behavior of the system, optimizing performance, and ensuring efficient operation.

## 3. Components of a Crank Slider Mechanism

To conduct a velocity analysis, it’s essential to understand the components involved:

**Crank**: The rotating part connected to the driving source, such as a motor.**Connecting Rod**: Links the crank to the sliding block, transferring motion between them.**Sliding Block**: Moves linearly within a guide as the crank rotates, completing the conversion of motion.

elocity analysis of a crank-slider mechanism can be performed using both analytical and graphical methods. Here’s a breakdown of each approach:

### 1. **Analytical Method**

The analytical method involves mathematical calculations and equations to determine the velocities of various parts in the mechanism.

#### Steps:

**Define Parameters and Setup Coordinates**- Define the lengths of the crank (AB), connecting rod (BC), and slider (CD).
- Establish a coordinate system, typically with the origin at the fixed point of the crank.

**Determine the Position of the Slider**- Use trigonometric relationships to express the position of the slider (CD) as a function of the crank angle θ\thetaθ.
- For example: x=L1cosθ+L22−(L1sinθ)2x = L_1 \cos \theta + \sqrt{L_2^2 – (L_1 \sin \theta)^2}x=L1cosθ+L22−(L1sinθ)2
- Here, xxx is the position of the slider, L1L_1L1 is the crank length, L2L_2L2 is the connecting rod length, and θ\thetaθ is the crank angle.

**Calculate the Velocity of the Crank**- The velocity of point B (end of the crank) is given by: vB=L1ωv_B = L_1 \omegavB=L1ω
- Here, ω\omegaω is the angular velocity of the crank.

**Calculate the Velocity of the Slider**- Differentiate the position equation of the slider with respect to time to find its velocity: vCD=ddt[L1cosθ+L22−(L1sinθ)2]v_{CD} = \frac{d}{dt} \left[ L_1 \cos \theta + \sqrt{L_2^2 – (L_1 \sin \theta)^2} \right]vCD=dtd[L1cosθ+L22−(L1sinθ)2]
- This involves using the chain rule to include the crank’s angular velocity ω\omegaω: vCD=−L1ωsinθ+L12ωsinθcosθL22−(L1sinθ)2v_{CD} = -L_1 \omega \sin \theta + \frac{L_1^2 \omega \sin \theta \cos \theta}{\sqrt{L_2^2 – (L_1 \sin \theta)^2}}vCD=−L1ωsinθ+L22−(L1sinθ)2L12ωsinθcosθ

**Calculate the Velocity of the Connecting Rod**- Use vector analysis or the velocity triangle method to determine the velocity of the connecting rod: vBC=vB−vCv_{BC} = v_B – v_CvBC=vB−vC
- Where vBv_BvB is the velocity of point B, and vCv_CvC is the velocity of point C.

**Check Consistency**- Ensure that the velocities calculated are consistent with the mechanism’s constraints and geometry.

### 2. **Graphical Method**

The graphical method involves drawing and analyzing the velocity diagram of the mechanism to determine the velocities.

#### Steps:

**Draw the Mechanism**- Create a scaled diagram of the crank-slider mechanism, showing all the components (crank, connecting rod, slider) in their relative positions.

**Draw the Velocity Diagram**- Represent the crank’s angular velocity ω\omegaω as a vector originating from the crank’s center. Draw this vector to scale.
- Use the crank’s angular velocity to determine the linear velocity of the crank’s end point (B).

**Construct the Velocity Triangle**- Construct a velocity triangle by drawing the vector representing the velocity of point B and the vector representing the velocity of the slider (CD).
- Use geometric construction to find the velocity of the connecting rod (BC). The connecting rod’s velocity is found by subtracting the velocity vector of the slider from the velocity vector of the crank’s end.

**Solve for Velocities**- Use the geometry of the velocity triangle to solve for the magnitudes and directions of the velocities of the connecting rod and slider.
- This involves measuring the angles and lengths on the velocity diagram and applying trigonometric relationships.

**Verify the Results**- Check that the graphical results align with the mechanism’s geometry and kinematic constraints.

### Summary

**Analytical Method:**

**Mathematical Approach:**Use equations and differentiation to find velocities.**Steps Include:**Position determination, velocity calculation, and verification.

**Graphical Method:**

**Visual Approach:**Draw the mechanism and velocity diagram.**Steps Include:**Constructing the velocity triangle, solving for velocities using geometry, and verification.

Both methods provide complementary insights into the velocity characteristics of the crank-slider mechanism. The analytical method provides precise calculations, while the graphical method offers a visual understanding of the relationships between velocities.

## 5. Importance of Results

Conducting a velocity analysis helps in:

**Optimizing Design**: Ensuring the mechanism operates efficiently and meets performance requirements.**Predicting Dynamic Behavior**: Understanding how components move and interact under different conditions.**Enhancing Durability**: Identifying potential issues such as excessive wear or vibration, and mitigating them through design adjustments.

## 6. Case Studies and Examples

### Case Study 1: Internal Combustion Engine

In an internal combustion engine, the crank slider mechanism converts the piston’s linear motion into rotational motion, driving the vehicle.

### Case Study 2: Reciprocating Pump

A reciprocating pump uses a crank slider mechanism to convert the rotational motion of a motor into the linear motion required to pump fluids.

### Example 3: Punch Press

A punch press employs a crank slider to convert rotary motion into the linear motion necessary to shape or cut materials.

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Understanding the velocity analysis of a crank slider mechanism is vital for designing efficient and reliable mechanical systems. By following the steps outlined above, engineers can ensure their mechanisms perform optimally and meet the demands of their applications. For a deeper dive into velocity analysis techniques and more case studies, stay tuned to our upcoming articles or reach out to our engineering experts.

Happy analyzing!