Unit 4: Forward Kinematics - Practice Quiz

1 What does forward kinematics determine for a robot?

2 How many revolute joints are considered in a two-axis planar articulated robot?

3 In a planar robot, the motion of the links mainly occurs in which type of space?

4 Which quantities are normally required to calculate the forward kinematics of a two-link planar robot?

5 For a two-link planar robot, which expression represents the -coordinate of the end effector?

6 For a two-link planar robot, which expression represents the -coordinate of the end effector?

7 In the equation , what does the sum represent for the second link?

8 What is the usual unit for measuring joint angles in a forward kinematics calculation?

9 What is the main purpose of the analytical method for planar forward kinematics?

10 What does DH stand for in robot kinematics?

11 How many standard parameters are used for each link in the Denavit-Hartenberg convention?

12 Which DH parameter represents the length of a link along the common normal?

13 Which DH parameter represents the twist angle between two joint axes?

14 Which DH parameter represents the distance along a joint axis?

15 Which DH parameter usually represents the variable angle of a revolute joint?

16 What is the purpose of assigning coordinate frames in the DH method?

17 In DH-based forward kinematics, what is done with the individual transformation matrices?

18 What does the final homogeneous transformation matrix provide in forward kinematics?

19 If both joint angles of a two-link planar robot are zero, how are the links commonly positioned?

20 Which item is a physical parameter needed when modeling the Orangewood Robotic Arm?

21 For a two-link planar robot with link lengths cm and cm, joint angles and , what is the end-effector position using the analytical forward-kinematics equations?

22 A two-axis planar arm has cm, cm, , and . What is the Cartesian position of the end effector?

23 In a planar two-link robot, the second joint angle is measured relative to the first link. Which angle determines the absolute orientation of the second link?

24 For cm, cm, , and , where is the end effector located?

25 Which homogeneous transformation matrix correctly represents a planar revolute joint followed by a link of length ?

26 For a two-link planar arm, the analytical expression for the -coordinate is . What does the second term represent?

27 Using standard DH parameters for a planar two-revolute robot, which parameter is generally nonzero for each link when the joint axes are parallel and the links lie in the plane?

28 Assume a DH model with , , , and . What is the position portion of the resulting transformation from base to end effector?

29 An Orangewood Robotic Arm is calibrated with link lengths cm and cm. At and , what reach should forward kinematics predict?

30 If changes while remains fixed in a two-axis planar arm, which point remains fixed ideally?

31 For a planar arm with cm, cm, and , , what is the approximate end-effector position?

32 A measured Orangewood arm configuration gives cm, cm, , and . Which end-effector orientation and position are expected?

33 When comparing analytical and DH forward kinematics for the same two-axis planar arm, what result should be obtained if both models use consistent frames and angle conventions?

34 A DH implementation produces the correct end-effector position for but an incorrect position for nonzero . Which modeling issue is most likely?

35 For cm, cm, , and , what is the predicted end-effector coordinate?

36 Which expression gives the end-effector orientation of a two-revolute planar robot relative to the base frame?

37 An arm has cm, cm, , and . What is the approximate position of the joint between the two links?

38 In a homogeneous transformation for a planar robot, what do the last column entries in the first two rows represent?

39 Suppose the first link length in an Orangewood Robotic Arm model is increased while both joint angles remain unchanged. Which forward-kinematics effect is expected?

40 For cm, cm, , and , what is the end-effector position?

41 For a two-link planar arm with link lengths and and joint angles measured counterclockwise from the positive -axis, which transformation correctly gives the end-effector position?

42 Using standard planar revolute-joint DH parameters, which homogeneous matrix represents a link with joint angle , link length , and zero twist and offset?

43 Let mm, mm, , and . What is the end-effector position under the analytical model?

44 For mm, mm, , and , which end-effector coordinate is correct?

45 The product of the two standard DH matrices for a planar arm has what upper-left rotation block and translation column?

46 If the Orangewood arm reports joint angles relative to its zero pose, but the physical zero pose has offsets and , which substitution should be made before applying forward kinematics?

47 For a planar two-link arm, the end-effector orientation is . If increases by and decreases by , what happens to ?

48 Which condition makes the planar two-link position Jacobian singular, assuming nonzero link lengths?

49 A DH implementation produces instead of . What is the most likely modeling error?

50 Suppose the base frame is rotated by a fixed angle relative to the laboratory frame. How should the planar analytical position be transformed into laboratory coordinates?

51 For mm, mm, and angles , what is the correct endpoint?

52 Under the standard DH convention, which parameter change correctly models a constant vertical displacement of the entire planar arm base?

53 If the second Orangewood joint is physically oriented so that positive commanded motion bends opposite to the mathematical convention, which corrected angle should appear in the model?

54 An arm has mm and mm. At and , which endpoint is predicted?

55 For a two-link arm, the first joint is fixed at and the second joint varies. Which statement describes the endpoint locus?

56 A measured configuration gives , , mm. What is the end-effector orientation and position?

57 Which matrix property is the strongest quick check that a computed homogeneous transform represents a proper planar rigid-body rotation?

58 A software implementation uses degrees in the user interface but passes and directly to a language trigonometric function that expects radians. What is the primary consequence?

59 For an Orangewood arm with a tool offset along the final link direction, which endpoint formula is correct?

60 If the two DH link lengths are accidentally swapped, which configuration is most useful for detecting the error experimentally?