1. Mehdi Ghayoumi MSB rm 160 mghayoum@kent.edu Ofc hr: Thur, 11-12:30a Robotic Concepts

2. Announcements: Today we talk about introduction in robotic HW #2 is available now due to Monday Sep-07 Office Hours: Tur: 11-12:30 Room 160 MSB

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4. Robot kinematics Robot kinematics studies the relationship between the dimensions and connectivity of kinematic chains and the position, velocity and acceleration of each of the links in the robotic system, in order to plan and control movement and to compute actuator forces and torques.kinematicsvelocityaccelerationactuatortorques

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10. Matrix A matrix is any doubly subscripted array of elements arranged in rows and columns. Robotic Concepts

11. Row Vector [1 x n] matrix Robotic Concepts

12. Column Vector [m x 1] matrix Robotic Concepts

13. Square Matrix Same number of rows and columns Robotic Concepts

14. Identity Matrix Square matrix with ones on the diagonal and zeros elsewhere. Robotic Concepts

15. Transpose Matrix Rows become columns and columns become rows Robotic Concepts

16. Matrix Addition and Subtraction A new matrix C may be defined as the additive combination of matrices A and B where: C = A + B is defined by: Note: all three matrices are of the same dimension Robotic Concepts

17. Addition If and then Robotic Concepts

18. Matrix Addition Example Robotic Concepts

19. Matrix Subtraction C = A - B Is defined by Robotic Concepts

20. Matrix Multiplication [r x c] and [s x d] c = s Robotic Concepts

21. Computation: A x B = C [2 x 2] [2 x 3] Robotic Concepts

22. [3 x 2][2 x 3] A and B can be multiplied [3 x 3] Robotic Concepts

23. Matrix Inversion Like a reciprocal in scalar math Like the number one in scalar math Robotic Concepts

24. For a XxX square matrix: The inverse matrix is: E.g.: 2x2 matrix: Robotic Concepts

25. a b c d det(A) = = ad - bc [ ] Robotic Concepts

27. X =A -1 B To find A -1 Need to find determinant of matrix A From earlier (2 -2) – (3 1) = -4 – 3 = -7 So determinant is -7 Linear Algebra & Matrices, MfD 2009 Robotic Concepts

28. Degree of freedom The number of degrees of freedom is defined as the number of independent coordinates which are necessary for the complete description of the position of a mass particle. 1. Mass particles 2.Rigid bodies

29. Robotic Concepts Degree of freedom

30. Robotic Concepts Degree of freedom

31. Robotic Concepts Degree of freedom

32. Robotic Concepts Degree of freedom A rigid body, has six degrees of freedom: 1.Three translations (the position of the body), 2.Three rotations(the orientation of the body).

33. Robotic Concepts Translational transformation

34. Robotic Concepts Translational transformation d = ai+bj+ck,

35. Robotic Concepts A translational displacement of vector q for a distance d is obtained by multiplying the vector q with the matrix H

36. Robotic Concepts Rotational transformation

37. Robotic Concepts Rotational transformation

38. Robotic Concepts Rotational transformation

39. Robotic Concepts Rotational transformation

40. Robotic Concepts Rotational transformation

41. Robotic Concepts we wish to determine the vector w which is obtained by rotating the vector u = 7i+3j+0k for 90 ◦ in the counter clockwise i.e. positive direction around the z axis. As cos90 ◦ = 0 and sin90 ◦ = 1, it is not difficult to determine the matrix describing Rot(z,90 ◦ ) and multiplying it by the vector u.

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43. Pose and displacement

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45. Robot manipulator The robot manipulator consists of : 1. A robot arm, 2. A robot wrist, 3. A robot gripper.

46. Robotic Concepts Robot manipulator The task of the robot manipulator is to place an object grasped by the gripper into an arbitrary pose. The task of the robot arm is to provide the desired position of the robot end point. The task of the robot wrist is to enable the required orientation of the object grasped by the robot gripper.

47. Robotic Concepts Robot manipulator In robotics the joint angles are denoted by the Greek letter ϑ. The relative position between the two segments is measured as a distance. The distance is denoted by the letter d.

48. Robotic Concepts Robot manipulator

49. Robotic Concepts Robot arms On the market we find 5 commercially available structures of robot arms: Anthropomorphic, Spherical, SCARA, Cylindrical, Cartesian.

50. Robotic Concepts Robot arms Anthropomorphic, The anthropomorphic robot arm has all three joints of the rotational type (RRR). Among the robot arms it resembles the human arm to the largest extent. The second joint axis is perpendicular to the first one, while the third joint axis is parallel to the second one.

51. Robotic Concepts Robot arms Spherical, The spherical robot arm has two rotational and one translational degree of freedom (RRT). The second joint axis is perpendicular to the first one and the third axis is perpendicular to the second one.

52. Robotic Concepts Robot arms SCARA, The SCARA (Selective Compliant Articulated Robot for Assembly) robot arm appeared relatively late in the development of industrial robotics. It is predominantly aimed for industrial processes of assembly. Two joints are rotational and one is translational (RRT). The axes of all three joints are parallel.

53. Robotic Concepts Robot arms Cylindrical, The cylindrical shape of the workspace is even more evident with the cylindrical robot arm. This robot has one rotational and two translational degrees of freedom (RTT). The axis of the second joint is parallel to the first axis, while the third joint axis is perpendicular to the second one.

54. Robotic Concepts Robot arms Cartesian. The cartesian robot arm has all three joints of the translational type (TTT). The joint axes are perpendicular one to another. Cartesian robot arms are known for high accuracy, while the special structure of gantry robots is suitable for manipulation of heavy objects.

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58. Seiko RT3300 Robot Robotic Concepts

60. Thank you!