Docstoc

Planar Kinematics of a Rigid Body20104511514

Document Sample
Planar Kinematics of a Rigid Body20104511514 Powered By Docstoc
					Kinematics of a Rigid Body: Basic Concept



 1. Relative motion
 2. Classification of problems
 3. GE226 General Equation




                 ME 316 Handout 2           1
           Relative Motion

1. Absolute Motion
 When the motion of an object is viewed by
 taking the earth as the reference body, the
 motion of the object is called the absolute
 motion.

                   ME 316 Handout 2            2
         Relative Motion


A reference object

                                        An object
       The earth



                            “Absolute motion”
                     ME 316 Handout 2               3
         Relative Motion
2. Relative Motion

 The reference object is another object, say
 B. The motion of A is viewed with
 reference to B.

  B: reference body                   A/B

                   ME 316 Handout 2            4
        Relative Motion

The relative motion of objects A and B can
also be a general planar motion (i.e., the
translation plus a rotation around a point on
the object).



                 ME 316 Handout 2               5
Relative
Motion

3. Relative

motion

equation




              ME 316 Handout 2   6
           Relative Motion
Relative rotation (B: reference body)


         A / B   A  B
                                        Absolute angular
Relative angular                        velocity of body B
velocity         Absolute angular
                 velocity of body A
                     ME 316 Handout 2                  7
        Relative Motion


 AB      the angular velocity of the
          assembly of A and B.


A/ B     the relative angular velocity
          of object A with respect to
          object B


             ME 316 Handout 2             8
            Relative Motion
Relative translation (B: reference body)

                                      Relative
                                      Translation is
                                      measured by two
                                      points selected
                                      from body A and
                                      body B,
                                      respectively, PA
                                      and PB in the left
                                      figure
                   ME 316 Handout 2                    9
             Relative Motion

Relative translation (B: reference body)



      VA / B (T )  VPA/ PB(T )  VPA  VPB




                     ME 316 Handout 2         10
                  Relative Motion
When two objects are in
contact, at their contact point
(PA and PB), the relative                  A
                                                    B
translation between these two
points are given:
             
           
   VPA / PB(T )  VPA  VPB                    PA
                                                    PB
                                           A
The direction of this relative                      B
translation is along the rod.
                        ME 316 Handout 2                11
   Relative Motion: Example
Example
                                AB  2

                               B  0



            ME 316 Handout 2              12
           Relative Motion
• Question (a). What is the relative angular velocity
  between gear B and arm AB, in particular taking
  arm AB as a reference object?

• Question (b). What is the angular velocity of gear
  A if we have found that the relative angular
  velocity of gear A with respect to gear B is 0.5
  rad/sec clockwise?

                      ME 316 Handout 2                 13
        Relative Motion
Solution (to be filled)




                ME 316 Handout 2   14
         Relative Motion
Solution (to be filled)




                   ME 316 Handout 2   15
 Classification of Problems
Kinematic pair – Link



                   B                                  B

    A                                      A




           Body                                Link




                        ME 316 Handout 2                  16
   Classification of Problems
Kinematic pair – Joint
     Types of joints               Graphical Representation        Relative motion



   Revolute joint (or pair)                                         Relative rotation




   Sliding joint (or pair)                                         Relative translation



                                                        Fixed (no relative motion)
   Fixed joint (or pair)


                                                              Both relative rotation
   Point contact joint (or pair)                              and translation

                                   ME 316 Handout 2                                    17
Classification of Problems
All joints are a revolute joint




                        ME 316 Handout 2   18
Classification of Problems
Sliding pair but its axis is fixed




                          ME 316 Handout 2   19
 Classification of Problems
Point contact joint – the bar is fixed




                           ME 316 Handout 2   20
Classification of Problems
Point contact – both are moving




                        ME 316 Handout 2   21
Classification of Problems
Sliding pair – the sliding axis rotates




                           ME 316 Handout 2   22
  GE 226 General Equation

                             VB  VA   AB  r B / A

                   B
 A
                                  The distance between A
                                  and B will not change with
                                  respect to time.


GE226 Equation can only solve problems with Types 1-3

                       ME 316 Handout 2                        23

				
DOCUMENT INFO