Introduction, Couplings, DoFs, 2-8 Oct

Question 1

(Intro)
What is an Industrial Robot?

Answer 1

Industrial Robotic: An automatically controlled, reprogrammable, multipurpose manipulator, programmable in 3 or more axes, which can be either fixed in place or mobile for use in industrial automation applications.

Industrial Robotic System:
A system comprising:
* Industrial Robot
* End-effector(s)
* Any machinery, equipment, devices, external auxiliary axes or sensors supporting the robot performing its task

Question 2

Industrial Robot

Answer 2

Mechanical Features related to:
* Links
* Couplings
* Degrees of freedom
* Drives (actuated joints)

Robot Classification
* Architecture (serial/parallel)
* Arm (bearing structure)
* Wrist
* End-effector

Question 3

Our first target

Answer 3

Giving a description of the position and orientation of the end-effector with respect to the absolute reference frame.

Mathematical Instrument: transformation matrix
* End-effector
* Each link of the robot
* Frame

Question 4

Position Kinematics

Answer 4

Forward Kinematics:
* Joint Space
* Cartesian Space
* Denavit Hartenberg Notation

Inverse Kinematics:
* Closed form solution
* Iterative methods
* Workspace

Question 5

Differential Kinematics

Answer 5

Velocity Jacobian Matrix:
* Relationship between joint velocities and cartesian velocities
* Analysis of kinematic singularities
* Inverse position kinematics
* Inverse dynamics (kinetostatics)

Question 6

Trajectory Planning

Answer 6

Motion laws:
* Trapezoidal profile
* Polinomial profile
* Some other profiles

Cartesian space and joint space
Point to point motion
Motion in N points

Question 7

Robot Programming (Adept V+ Language)

Question 8

(Couplings)
Mechanism Parts

Answer 8

Each element of a mechanism is called link
More specific names that also describe the motion of the link:
1. Crank (rotate 360˘)
2. Connecting rod (rotate and translate)
3. Rocker ( rotate < 360˘)
4. Frame (no movement)

Question 9

Couplings (Kinematic pairs)

Answer 9

Two links that are connected to each other, so that a relative motion is possible, form a kinematic pair (kinematic joint)

• Revolute pair
• Prismatic pair
• Flanged joint (non kinematic pair)

Question 10

Conjugate surface

Answer 10

A relative motion can be achieved thanks to the sliding of the conjugate surfaces

Question 11

Types of kinematic pair

Answer 11

• Form Closed
• Force Closed

Question 12

Couplings and Classes

Answer 12

-A free rigid body has 6 dofs (3 rotations and 3 translation)
- A kinematic pair between two links, reduces (limits) the numbers of dof of the relative motion. (A coupling is a constraint)
- The Class of a kinematic pair is the number of the dofs that are allowed by the coupling.

Question 13

Lower Pairs (surface contact)

Answer 13

• Revolute pair: 1R, Class 1
• Prismatic pair: 1T, Class 1
• Helical pair: 1R + 1T, Class 1
• Cylindrical pair: 1R, 1T, Class 2
• Spherical pair: 3R, Class 3
• Plane pair: 2 T, 1R, Class 3

Question 14

Higher pairs (also linear and point contact)

Answer 14

• Slotted Spherical pair: 2R, Class 2
• Planar Cam pair: 1R, 1T, Class 2
• Sphere Slotted Cylinder pair: 2R, 1T Class 3
• Sphere Cylinder pair [in line joint]: 3R, 1T Class 4
• Cylinder Plane pair: 2R, 2T Class 4
• Sphere plane pair: 3R, 2T Class 5

Question 15

(Degrees of Freedom)
Definitions

Answer 15

• Planar mechanism: a mechanism whose links have velocity vectors that are parallel to the same plane (called plane of motion). Two transitions and one rotation are allowed. Which pairs can we use:
  * Revolute pair
  * Prismatic pair
  * Cam pair
  Plane pair (NO!)
• Articulated mechanism: a mechanism made up of kinematic pairs that belong to class 1
• Kinematic chain: set of links connected by kinematic pairs
• Mechanism: a kinematic chain where the frame is defined
  
  • Different mechanisms can derive from the same chain (choice of the frame)
    A kinematic chain can be opened or closed
    Members can be binary, ternary, etc. (number of pairs)
• Kinematic scheme: a representation of the mechanism that keeps dimensions and degrees of mobility

Question 16

Kutzbach Equation (spatial mechanisms)

Answer 16

n = 6(m-1) - 5c1 - 4c2 - 3c3 - 2c4 - c5

n => number of degreed of freedom
m => number of links (frame included)
ci => number of kinematics pairs that belongs to the class i

Question 17

Grubler Equation (planar mechanisms)

Answer 17

n = 3(m-1) -2c1 - c2

n => number of degrees of freedom
m => number of links (frame included)
ci => number of kinematic pairs that belongs to the class i

Question 18

Cases where these equations may fail

Answer 18

• Wrong application (spatial-planar)
• Redundant constraint (kinematic pairs)
• Hyperstatic mechanism