What is an industrial robot?

Transcription

1 What is an industrial robot? A robot is CFIDV 02CFIC CY A kinematic chain A multi-body dynamical system A system with motors and drives A system with digital and analogic sensors An electronic system A supervised and controlled system A software driven system Therefore a mechatronic system Basilio Bona DAUIN Politecnico di Torino 002/1

2 Industrial robotics CY 02CFIC CFIDV Scope: object manipulation Robots are often called Industrial Manipulators Robots/robotic arms Usually the robot base is fixed or moves along rails The previous COMAU robot at LabRob Basilio Bona DAUIN Politecnico di Torino 002/2

3 Prerequisites CFIDV 02CFIC CY Read Chapter 2 of the textbook Reference systems Vectors Matrices Rotations, translations, roto-translations Homogeneous representation of vectors and matrices Basilio Bona DAUIN Politecnico di Torino 003/3

4 Reference Systems/Frames Three unit vectors (versors) mutually orthogonal in 3D space CFIDV 02CFIC CY Right-hand reference frames (RHRF) obey right hand rule Color code RGB right hand rule k k = i j i j When the fingers go from i to j the thumb is aligned with k Basilio Bona DAUIN Politecnico di Torino 003/4

5 Reference Systems/Frames We call this the cavatappi (corkscrew) rule CFIDV 02CFIC CY k = i j j R i i This is also called a CARTESIAN FRAME Basilio Bona DAUIN Politecnico di Torino 003/5

6 Reference frames and rigid bodies 02CFIC CY CFIDV Every rigid id body is defined d by a RHRF, the so-called body frame (BF) All points in the rigid body are defined by suitable vectors in the body frame Basilio Bona DAUIN Politecnico di Torino 003/6

7 Vectors and Matrices CFIDV 02CFIC CY Introductory notes on vectors and matrices can be found here VECTORS lit it/m t i /01CFI/ /Slid /V i df MATRICES Basilio Bona DAUIN Politecnico di Torino 003/7

8 Kinematics 02CFIC CY CFIDV Kinematics allow to represent positions, velocities and accelerations of multibody points, independently from the causes that generate them (i.e., forces and torques) In order to describe the kinematics of manipulators or mobile robots, it is necessary to define the concept of kinematic chain A kinematic chain is a series of ideal arms connected by ideal joints Flexible Arm M = 102 [g], J = 530 [Kgmm^2], L = 25 [cm] M = 9.5 [g], J = [Kgmm^2], L = 2.5 [cm] M = 192 [g], J = 3595 [Kgmm^2], L = 47.5 [cm] Basilio Bona DAUIN Politecnico di Torino 003/8

9 Is the human arm a kinematic chain? CFIDV 02CFIC CY Wit Wrist Arm What is this? The human arm + wrist has 7 dof A redundant arm But it is not ideal, since it is composed by muscles, bones and other tissues, is not a rigid body, the joint are elastic, etc. Basilio Bona DAUIN Politecnico di Torino 003/9

10 Kinematic chain CFIDV 02CFIC CY A kinematic chain KC is composed by a variable number of Arms/links (rigid and ideal) Joints (rigid and ideal) It is defined only as a geometric entity (no mass, friction, etc.) It has degrees of motion and degrees of freedom (DOF) One must be able to fix on each arm a RF -> DH conventions One must be able to describe every possible point in a given RF Basilio Bona DAUIN Politecnico di Torino 003/10

11 Kinematic chain 02CFIC CY A multi-body structure composed by ideal rigid arms/links (no mass and other dynamic properties), linked to other arms by ideal joints that allow a relative motion between two successive arms CFIDV Joints 4, 5, 6 Arm 1 Link 3 Joint 3 Arm 2 Joint 2 Joint 1 Joints allow a single degree of motion between connected links Joints may be Rotoidal or rotation or rotational joints allow a relative rotation between arms Prismatic or translation joints allow a relative translation between arms Basilio Bona DAUIN Politecnico di Torino 003/11

12 Kinematic chain 02CFIC CY CA 01CFIDV OBOTIC RO wrist shoulder wrist shoulder Basilio Bona DAUIN Politecnico di Torino 003/12

13 Howwedrawjointsandlinks? we and Rotation Joints 02CFIC CY Rotation joints are draw in 3D perspective as small cylinders with axes aligned along each rotation axis k CFIDV axis is normal to the plane pointing toward the observer Rotation joints are draw in 2D as small circles or small hourglasses k i i j j Basilio Bona DAUIN Politecnico di Torino 003/13

14 ROBOTICA 01CFIDV 02CFICY Example Basilio Bona DAUIN Politecnico di Torino 003/14

15 CFIDV 02CFIC CY Prismatic Joints Prismatic joints are draw in 3D perspective as small boxes with each axis aligned along the translation axis Prismatic joints are draw in 2D as small squares with a point in their centres or as small rectangles with a line showing the two successive links k i j Basilio Bona DAUIN Politecnico di Torino 003/15

16 ROBOTICA 01CFIDV 02CFICY Example Basilio Bona DAUIN Politecnico di Torino 003/16

17 CY CA 01CFIDV 02CFIC OBOTIC RO Another example Basilio Bona DAUIN Politecnico di Torino 003/17

18 Kinematic chain CFIDV 02CFIC CY The COMAU robot seen as an ideal kinematic chain Basilio Bona DAUIN Politecnico di Torino 003/18

19 Kinematic representation CFIDV 02CFIC CY q 6 q 5 q 3 q 4 The joint motion produces a motion in Cartesian 3D space. One must be able to describe the relation between the two representations Joint space vs Task space q 2 q 1 Basilio Bona DAUIN Politecnico di Torino 003/19

20 Joint space and task space 02CFIC CY Task Space (Cartesian) z Joint space CFIDV x 6 direct 3 y inverse q 1 q n q 2 direct kinematics is easier than inverse kinematics Basilio Bona DAUIN Politecnico di Torino 003/20

21 RO OBOTIC CA 01CFIDV 02CFIC CY Task Space Task Space Operational Space Workspace p Are synonymous Basilio Bona DAUIN Politecnico di Torino 003/21

22 Degrees of motion and degrees of freedom CFIDV 02CFIC CY The degrees of motion (dom, as they are called) count the number of prismatic/rotation joints (active, i.e., motor-driven or passive) The degrees of freedom (dof, as they are called) count the number of free parameters of the considered body Dofs may be referred to manipulator, when they count what it can do with its center point, or to the task when measure what is required by the application Basilio Bona DAUIN Politecnico di Torino 003/22

23 Degrees of motion and degrees of freedom Joint 3 02CFIC CY Joint 1 TCP Tool Center Point CFIDV Joint 4 Joint 2 Base The KC has 4 degrees of motion since there are 4 rotating joints An object in a plane has only 3 dof (two positions + one angle) Therefore this KC is redundant (redundancy 4-3 = 1). If the task requires only the object positioning, with no particular constraint on orientation, ti the dof will reduce to 2 and the redundancy d increases to 4-2=2 2 Basilio Bona DAUIN Politecnico di Torino 003/23

24 02CFIC CY CA 01CFIDV OBOTIC RO Often one reads that a robot control is able to manage, e.g., 8 dof. This sentence should be correctly understood, since it means that the robot is able to control 8 degrees of motion. In the example below the robot has 5 dof and 5 dom, and the additional 3 dom on the rotating fixture are useful only for part machining. The task on parts on the rotating fixtures requires 5 or 6 dof. Example of a robot with a slave rotating ti fixture with additional degrees of motion Basilio Bona DAUIN Politecnico di Torino 003/24

25 CFIDV 02CFIC CY In this example the robot has 5 dom, + 1 of the translating base + 2 of the two rotating fixtures. In total 5+1+2=8 dom, and the task maybe 5 or 6 dof Robot with a translating base Basilio Bona DAUIN Politecnico di Torino 003/25