Robotics. SAAST Robotics Robot Arms

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1 SAAST Robotics 008 Robot Arms Vijay Kumar Professor of Mechanical Engineering and Applied Mechanics and Professor of Computer and Information Science University of Pennsylvania

2 Topics Types of robot arms Serial chain and parallel chain Examples of industrial robots Degrees of freedom Geometry: workspace Kinematics: motion analysis Direct kinematics and inverse kinematics Robot programming Dynamics: payload/strength

3 Topics Types of robot arms Serial chain and parallel chain Examples of industrial robots Degrees of freedom Geometry: workspace Kinematics: motion analysis Direct kinematics and inverse kinematics Robot programming Dynamics: payload/strength

4 Definitions Robotics Types of Robot Arms Kinematic chain A system of rigid bodies connected together by joints. A chain is called closed if it forms a closed loop. A chain that is not closed is called an open chain. Serial chain If each link of an open chain except the first and the last link is connected to two other links it is called a serial chain. Serial chain manipulator The links/joints of the manipulator form a serial chain Parallel chain manipulator Multiple serial chains arranged in parallel

5 Topics Types of robot arms Serial chain and parallel chain Examples of industrial robots Degrees of freedom Geometry: workspace Kinematics: motion analysis Direct kinematics and inverse kinematics Robot programming Dynamics: payload/strength

6 Examples Kuka Cincinnati Milacron T 3 Staubli (formerly Unimate PUMA)

7 SCORBOT-ER V Five axes Plus Gripper (on/off) Jt 5 Jt 3 Jt 4 Motor Jt Jt Motor

8 Topics Types of robot arms Serial chain and parallel chain Examples of industrial robots Degrees of freedom Geometry: workspace Kinematics: motion analysis Direct kinematics and inverse kinematics Robot programming Dynamics: payload/strength

9 Degrees of Freedom Degree of freedom of a joint The number of independent motions obtained by fixing all other joints Rotary or revolute joint () Translatory or prismatic joint () Spherical joint (3) Degrees of freedom of a serial chain manipulator Serial chain Add up the degrees of freedom (f i ) of each joint M = n! i= f i

10 The Planar 3-R manipulator Planar kinematic chain All joints are revolute (f i = ) What is the number of degrees of freedom? END-EFFECTOR Link 3 R Link R Joint 3 Link R Joint Joint ACTUATORS

11 Examples: Degrees of Freedom The Adept 850 Palletizer The Beckman Coulter ORCA Four degrees of freedom Five degrees of freedom

12 Degrees of Freedom of a Planar Parallel Manipulator Number of degrees of freedom n j f i M = 3 j f i i= ( n " j " ) +! number of links (must include the ground) number of joints between the links degree of freedom of joint i Also applicable to serial chains manipulators and linkages

13 Examples: Degrees of Freedom Planar serial chain number of links, n = 4 number of joints, j = 3 joint dof, f i = Planar parallel manipulator number of links, n = 8 number of joints, j = 9 joint dof, f i = 4 END-EFFECTOR END-EFFECTOR R R P ACTUATORS ACTUATORS 5 M = 3 j f i i= ( n " j " ) +!

Spatial Parallel Manipulator Ingersoll Rand machine tool (Stewart Platform) number of links, n = 0 number of joints, j = 4 connectivity, f i = or 3 LEG 3 END EFFECTOR

14 Spatial Parallel Manipulator Ingersoll Rand machine tool (Stewart Platform) number of links, n = 0 number of joints, j = 4 connectivity, f i = or 3 LEG 3 END EFFECTOR LEG 4 END EFFECTOR S Leg 5 Leg 4 LEG Leg 6 LEG 5 P Leg 3 LEG Leg Leg LEG 6 R R BASE BASE M = 6 ( n " j " ) +! j i= f i M = ( 9! 4) = LEG NO. i Note: 6 and not 3

15 The Khepri Robot

16 Six Degree-of-Freedom Manipulator ABB Flexpicker capable of pick and place operations per second Micromanipulator (PI Hexapod) ABB IRB 940 used for machining and cleaning of aluminium castings

17 Topics Types of robot arms Serial chain and parallel chain Examples of industrial robots Degrees of freedom Geometry: workspace Kinematics: motion analysis Direct kinematics and inverse kinematics Robot programming Dynamics: payload/strength

18 Robot Geometry Types of joints revolute (rotary) versus prismatic (sliding) elbow manipulator, SCARA manipulator, Gantry manipulator Type of workspace SCARA Gantry

19 Robot workspace or work envelope The set of points a reference point on the end effector (or the most distal link) can reach in three dimensions Regional structure Consists of proximal joints and links Positions the end effector Determines the workspace Orientation structure Consists of distal joints and links Orients the end effector

20 Robot Dexterity Optimal Geometry 3 mutually orthogonal axes Concurrent (intersecting at Q) Axis 4 Q Axis 5 Axis 6 P If there are no joint limits, the end effector can be rotated through 360 degrees about any axis passing through Q.

21 Reachable Workspace Two revolute joints axis perpendicular to axis P a a Axis Axis

22 Robot Geometry and Workspace Axis perpendicular to axis a P Axis a a a Axis Axis Geometry Workspace traced by point P

23 Robot Geometry and Workspace Two revolute joints axis parallel to axis P a Axis a Axis

24 Robot Geometry and Workspace Two revolute joints Geometry Top view of the workspace generated by the point P P a a a Axis Axis Axis a

25 Robot Geometry and Workspace Three revolute joints axis perpendicular to axis axis 3 parallel to axis P a a a 3 Axis Axis 3 Axis Axes and 3 generate an annulus Axis sweeps the annulus around the vertical

26 Robot Geometry and Workspace Three revolute joints axis perpendicular to axis axis 3 parallel to axis P a a a a 3 Axis Axis 3 Axis Workspace is an annulus swept around a vertical axis

27 Optimal Geometry for Fixed Length (L) The area of the annulus is maximized when a = a 3 (the annulus becomes a full circle) The volume of the torus generated by sweeping the circle about axis is maximized when a = 0 (the torus becomes a sphere) P a V = a = 3 3 4!L = 3 P L a 3 a a a 3 Axis Axis 3 a Axis 3 Axis Axis Axis

28 Scorbot

29 Topics Types of robot arms Serial chain and parallel chain Examples of industrial robots Degrees of freedom Geometry: workspace Kinematics: motion analysis Direct kinematics and inverse kinematics Robot programming Dynamics: payload/strength

30 Kinematics Direct Kinematics Given the (commanded) joint angles, find the end-effector position Inverse Kinematics Given the (desired) end-effector position, find the joint angles that correspond to the end-effector position

31 Modeling D y l 3 C φ 3 l φ B l A φ x

32 Relative Joint Angles D y l 3 θ 3 θ C l θ l A x B

33 Absolute and Relative D y l 3 C l φ 3 B φ l A φ absolute x D The commanded and measured joint angles are relative joint angles! y l 3 θ 3 θ θ relative x l A

34 Kinematic modeling Link Actuated joint End effector (EE) Reference point on EE REFERENCE POINT ( x,y) φ l Link 3 (EE) l 3 θ 3 Joint coordinates θ, θ, θ 3 End effector coordinates x, y, φ Link lengths (l i ) y l θ θ x Link Link

35 Kinematic transformations Direct kinematics Joint coordinates to end effector coordinates Why is it useful? Inverse kinematics End effector coordinates to joint coordinates Why is it useful?

36 Kinematics algorithms Direct kinematics Joint coordinates to end effector coordinates Sensors are located at the joints. DK algorithm is used to figure out where the robot is in 3-D space. Robot thinks in joint coordinates. Programmer/engineer thinks in world coordinates or end effector coordinates. Inverse kinematics End effector coordinates to joint coordinates Given a desired position and orientation of the EE, we want to be able to get the robot to move to the desired goal. IK algorithm used to obtain the joint coordinates. Essential for control.

37 Direct kinematics Transform joint coordinates to end effector coordinates REFERENCE POINT (x,y) φ l 3 θ 3 l y l θ θ x x = y = " = l l cos! sin! (! +! +! ) + l + l sin 3 cos (! +! ) + l3 cos(! +! +! 3) (! +! ) + l sin(! +! +! ) 3 3

38 Direct kinematics Transform joint coordinates to end effector coordinates x = y = z = " = l l d cos! sin! (! +! +! ) 3 + l + l cos sin (! +! 3) + l4 cos(! +! 3 +! 4) (! +! ) + l sin(! +! +! ) Adept palletizer: PRRR manipulator

39 Inverse kinematics Transform end effector coordinates to joint coordinates REFERENCE POINT (x,y) φ l 3 θ 3 l y l θ θ x x = y = " = l l cos! sin! (! +! +! ) + l + l sin 3 cos (! +! ) + l3 cos(! +! +! 3) (! +! ) + l sin(! +! +! ) 3 3 Given x, y, φ, solve for θ, θ, θ 3

40 Inverse kinematics (continued) + = * + ) cos REFERENCE POINT ( x,y) ( l 3 θ 3 φ & $ ( $ % ( x' + y' + l ( l ) l "! = a tan $ # x' + y' Q P + Q, P #!! " P + Q x " = x # l 3 cos$ y " = y # l 3 sin$ % ' & y l θ l ( ) ( ) P = "l x # Q = "l y # ( ) R = x # + y # + l " l θ x $! = atan & % y " # l sin!, l! 3 = " # (! +! ) x " # l cos! ' ) #! ( l

41 Inverse Kinematics There are two solutions to the inverse kinematics of a 3R manipulator REFERENCE POINT (x,y)! " =+ " =-

42 Direct and Inverse Kinematics Kinematics of truly 3-D manipulators is more complicated Matrix algebra required to describe three-dimensional rotations and translations Complexity of expressions grows with number of joints Control software must perform calculations in real-time At most several milliseconds Floating-point (not integer) arithmetic Update rate is between 500 0,000 Hz.

43 Topics Types of robot arms Serial chain and parallel chain Examples of industrial robots Degrees of freedom Geometry: workspace Kinematics: motion analysis Direct kinematics and inverse kinematics Robot programming Dynamics: payload/strength

roll/pitch Gripper control Open/close Programming Record positions

44 Programming by Teaching Joint control +/- individual joints Cartesian control +/- x, y, z directions Orientation control +/- roll/pitch Gripper control Open/close Programming Record positions Go to positions Set speed No guarantees on trajectory between taught positions

45 Topics Types of robot arms Serial chain and parallel chain Examples of industrial robots Degrees of freedom Geometry: workspace Kinematics: motion analysis Direct kinematics and inverse kinematics Robot programming Dynamics: payload/strength

46 Example: Scorbot Each axis powered by 5 oz. in motors, 70 Watts Transmission: Gears, timing belt Repeatability = +/- 0.0 (+/- 0.5 mm) Micro switches or limit switches for each motor kg payload, total mass kg Max speed = 3.6 in/sec (600 mm/sec)

47 Joint Torques and Payloads τ Δx Angular displacement, Δθ (radians) determined by the joint sensor Δθ a F End point displacement (meters) Δ x = a (meters) Δθ (radians) Note: degrees π/80 = radians Axis of Rotation Load force F newtons Motor torque (newton meters) required to resist the load τ = a (meters) x F newtons

EEE 187: Robotics Summary 2

1 EEE 187: Robotics Summary 2 09/05/2017 Robotic system components A robotic system has three major components: Actuators: the muscles of the robot Sensors: provide information about the environment and