Chapter 2, Problem 2.1P

Find three (or other number as assigned) of the following common devices. Sketch careful kinematic diagrams and find their total degrees of freedom.

1. An automobile hood hinge mechanism
2. An automobile hatchback lift mechanism
3. An electric can opener
4. A folding ironing board
5. A folding card able
6. A folding beach chair
7. A baby swing
8. A folding baby walker
9. A fancy corkscrew as shown in Figure P2-9
10. A windshield wiper mechanism
11. A dump truck dump mechanism
12. A trash truck dumpster mechanism
13. A pickup truck tailgate mechanism
14. An automobile jack
15. A collapsible auto radio antenna

To determine

To find:Kinematic diagrams and total DOF in an automobile hood hinge mechanism.

Explanation of Solution

Given information:

The initial conditions that are given are that of an automobile hood hinge mechanism

Calculation:

Here KutzbatchEquation is used to compute mobility (DOF) of the shown system below. An automobile mechanism systemcondition is as shown. $withhood\left(3\right)islinkedbody\left(1\right) tworockerlinks\left(2and4\right)$

  $\begin{array}{l}\begin{array}{l}NumberoflinksL=4\hfill \\ NumberoffulljointsJ1=4 \hfill \end{array}\\ \begin{array}{l}NumberofhalfjointsJ2=0\hfill \\ M=3\left(L-1\right)-2J1-J2\hfill \\ M=1\hfill \end{array}\end{array}$

  

To determine

To find:Kinematic diagrams and total DOF inan automobile hatchback lift mechanism.

Explanation of Solution

Given information:

The initial conditions that are given are that of An automobile hatchback lift mechanism.

Calculation:

Here Kutzbatch Equation is used to compute mobility (DOF) the models below. Here mainly considering the given mechanism of an automobile hatchback lift mechanism which having the $hatch\left(2\right)$ with the $body\left(1\right)$ linked body by lift arm, modeled as two $links\left(3and4\right)$ linkedbyslider joint

  $\begin{array}{l}\begin{array}{l}NumberoflinksL=4 \\ NumberoffulljointsJ1=4\end{array}\hfill \\ NumberofhalfjointsJ2=0 \hfill \\ M=3\left(L-1\right)-2J1-J2 M=1\hfill \end{array}$

  

To determine

To find:Kinematic diagrams and total DOF in the electric can opener.

Explanation of Solution

Given information:

The initial conditions that are given are that of electric opener has 2 DOF.

Calculation:

Here Kutzbatch Equation is used to compute mobility (DOF) the given mechanismbelow. Here mainly considering the given mechanism of an electric opener has 2 DOF

  $\begin{array}{l}\begin{array}{l}NumberoflinksL=4 \\ NumberoffulljointsJ1=3\end{array}\hfill \\ NumberofhalfjointsJ2=0 \hfill \\ M=3\left(L-1\right)-2J1-J2 M=2\hfill \end{array}$

  

To determine

To find:Kinematic diagrams and total DOF in a folding ironing board.

Explanation of Solution

Given information:

The initial conditions that are given are that of a folding ironing board

Calculation:

Here Kutzbatch Equation is used to compute mobility (DOF) the given mechanism below.Here mainly considering the given mechanism A folding ironing board with One leg joins pivot joint on board and the other is slider joint.

  

  $\begin{array}{l}NumberoflinksL=3 \hfill \\ NumberoffulljointsJ1=2\hfill \\ NumberofhalfjointsJ2=1\hfill \\ M=3\left(L-1\right)-2J1-J2 M=1\hfill \end{array}$

To determine

To find:Kinematic diagrams and total DOF in a folding card table.

Explanation of Solution

Given information:

The initial conditions that are given are that ofa folding card table.

Calculation:

Here Kutzbatch Equation is used to compute mobility (DOF) the given mechanism below. A folding card table having 7 DOF for considering 1 for individual leg, 2 for x-ylocation and one for angular orientation.

  

To determine

To find:Kinematic diagrams and total DOF in a folding beach chair.

Explanation of Solution

Given information:

The initial conditions that are given are that of a folding beach chair.

Calculation:

Here Kutzbatch Equation is used to compute mobility (DOF) the given mechanism below. A folding beach chair with ternary links having analysis below is Subtract 1 DOF forced stop.

  $\begin{array}{l}NumberoflinksL=6 \hfill \\ NumberoffulljointsJ1=7\hfill \\ NumberofhalfjointsJ2=0\hfill \\ M=3\left(L-1\right)-2J1-J2 M=1\hfill \end{array}$

  

To determine

To find:Kinematic diagrams and total DOF in a baby swing.

Explanation of Solution

Given information:

The initial conditions that are given are that ofa baby swing.

Calculation:

Here Kutzbatch Equation is used to compute mobility (DOF) the given mechanism below. A baby swing has 4 DOF,for swing 1 angular orientation w.r.t. frame, and 3 for location and orientation of the frame w.r.t. a 2-D frame.

  $\begin{array}{l}NumberoflinksL=4 \hfill \\ NumberoffulljointsJ1=3\hfill \\ NumberofhalfjointsJ2=0\hfill \\ M=3\left(L-1\right)-2J1-J2 M=2\hfill \end{array}$

  

To determine

To find:Kinematic diagrams and total DOF in a folding baby walker.

Explanation of Solution

Given information:

The initial conditions that are given are that ofA folding baby walker

Calculation:

Here Kutzbatch Equation is used to compute mobility (DOF) the given mechanism below. A folding baby walker having 4 DOF with considering of 1 degree with unfolded, and 3 for the walkerlocation and orientation w.r.t.a 2-D frame.

  $\begin{array}{l}NumberoflinksL=4 \hfill \\ NumberoffulljointsJ1=3\hfill \\ NumberofhalfjointsJ2=0\hfill \\ M=3\left(L-1\right)-2J1-J2 M=2\hfill \end{array}$

  

To determine

To find:Kinematic diagrams and total DOF in a fancy corkscrew.

Explanation of Solution

Given information:

The initial conditions that are given are that ofa fancy corkscrew.

Calculation:

Here Kutzbatch Equation is used to compute mobility (DOF) the given mechanism below. A fancy corkscrew having 2 DOF for screw rotated and arms rotate to translate w.r.t. screw.

  $\begin{array}{l}NumberoflinksL=4 \hfill \\ NumberoffulljointsJ1=3\hfill \\ NumberofhalfjointsJ2=0\hfill \\ M=3\left(L-1\right)-2J1-J2 M=2\hfill \end{array}$

To determine

To find:Kinematic diagrams and total DOF in a windshield wiper mechanism.

Explanation of Solution

Given information:

The initial conditions that are given are that of A windshield wiper mechanism.

Calculation:

Here Kutzbatch Equation is used to compute mobility (DOF) the given mechanism below.A windshield wiper mechanism has 1 DOF with considering of the wiper blades position w.r.t. a single input.

  $\begin{array}{l}NumberoflinksL=4 \hfill \\ NumberoffulljointsJ1=3\hfill \\ NumberofhalfjointsJ2=0\hfill \\ M=3\left(L-1\right)-2J1-J2 M=1\hfill \end{array}$

  

To determine

To find:Kinematic diagrams and total DOF in a dump truck mechanism.

Explanation of Solution

Given information:

The initial conditions that are given are that of. A dump-truck dump mechanism

Calculation:

Here Kutzbatch Equation is used to compute mobility (DOF) the given mechanism below.A dump-truck dump mechanism having 1 DOF for a angle of dump body for length of the hydraulic cylinder links w.r.t. the body truck.

  $\begin{array}{l}NumberoflinksL=4 \hfill \\ NumberoffulljointsJ1=3\hfill \\ NumberofhalfjointsJ2=0\hfill \\ M=3\left(L-1\right)-2J1-J2 M=1\hfill \end{array}$

  

To determine

To find:Kinematic diagrams and total DOF in a trash truck mechanism.

Explanation of Solution

Given information:

The initial conditions that are given are that ofA trash truck dumpster mechanism

Calculation:

Here Kutzbatch Equation is used to compute mobility (DOF) the given mechanism below. A trash truck dumpster mechanism having 2 DOF for generally a rotation and a translation.

  $\begin{array}{l}NumberoflinksL=4 \hfill \\ NumberoffulljointsJ1=2\hfill \\ NumberofhalfjointsJ2=0\hfill \\ M=3\left(L-1\right)-2J1-J2 M=2\hfill \end{array}$

  

To determine

To find:Kinematic diagrams and to find their total DOF in a trash truck tailgate mechanism.

Explanation of Solution

Given information:

The initial conditions that are given are that ofa pickup tailgate mechanism.

Calculation:

Here Kutzbatch Equation is used to compute mobility (DOF) the given mechanism below. A pickup tailgate mechanism having a 1 DOF.

  $\begin{array}{l}NumberoflinksL=4 \hfill \\ NumberoffulljointsJ1=3\hfill \\ NumberofhalfjointsJ2=0\hfill \\ M=3\left(L-1\right)-2J1-J2 M=1\hfill \end{array}$

  

To determine

To find:Kinematic diagrams and total DOF in an automobile jack.

Explanation of Solution

Given information:

The initial conditions that are given are that ofAn automobile jack mechanism.

Calculation:

Here Kutzbatch Equation is used to compute mobility (DOF) the given mechanism below. An automobile jack having 1 DOF for height jack and the other for the positionand orientation of the jack w.r.t. a 2-D frame.

  

, total4 DOF

  $\begin{array}{l}NumberoflinksL=4 \hfill \\ NumberoffulljointsJ1=2\hfill \\ NumberofhalfjointsJ2=0\hfill \\ M=3\left(L-1\right)-2J1-J2 M=2\hfill \end{array}$

To determine

To find:Kinematic diagrams and total DOF in a collapsible auto radio antenna.

Explanation of Solution

Given information:

The initial conditions that are given are that ofa collapsible auto radio antenna mechanism.

Calculation:

Here Kutzbatch Equation is used to compute mobility (DOF) the given mechanism below. Amany DOF with considering section for a collapsible auto radio antenna, its less one.

  $\begin{array}{l}NumberoflinksL=4 \hfill \\ NumberoffulljointsJ1=3\hfill \\ NumberofhalfjointsJ2=0\hfill \\ M=3\left(L-1\right)-2J1-J2 M=1\hfill \end{array}$