Back to Subject

Unit 5: Inverse Kinematics - Practice Quiz

ECE245 — Elements Of Robotics Laboratory 60 Questions
0 Correct 0 Wrong 60 Left
0/60

1 What does inverse kinematics determine for a robotic arm?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Easy
A. Battery capacity for a joint
B. Motor voltage for a fixed speed
C. Link weight for a desired position
D. Joint angles for a desired position

2 A two-axis planar articulated robot mainly moves in which type of workspace?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Easy
A. A fixed vertical surface
B. A one-dimensional line
C. A two-dimensional plane
D. A three-dimensional sphere

3 Which quantities are usually given in an inverse kinematics problem?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Easy
A. End-effector position
B. Robot brand and model
C. Motor color and size
D. Cable length and mass

4 For a two-link planar robot, what do and commonly represent?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Easy
A. The two link lengths
B. The two joint masses
C. The two sensor ranges
D. The two motor speeds

5 Which method uses a triangle formed by the robot links and the target point?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Easy
A. Frequency approach
B. Geometric approach
C. Thermal approach
D. Electrical approach

6 Which trigonometric rule is commonly used to calculate the second joint angle in a two-link planar robot?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Easy
A. Tangent rule only
B. Sine rule for speed
C. Pythagorean rule only
D. Cosine rule

7 What does the term usually describe in the planar robot coordinate system?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Easy
A. First link angle
B. Horizontal target position
C. Vertical target position
D. Second link length

8 What does the term usually describe in the planar robot coordinate system?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Easy
A. Horizontal target position
B. Vertical target position
C. First link length
D. Joint encoder type

9 Which function is useful for finding an angle from both and coordinates?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Easy
A.
B.
C.
D.

10 What is one common reason that a target point may be unreachable?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Easy
A. It lies outside the arm's reach
B. It is written in centimeters
C. It is located in the workspace
D. It has a positive value

11 For link lengths and , what is the maximum reach of a fully extended two-link planar arm?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Easy
A.
B.
C.
D.

12 What does a second inverse kinematics solution for the same target often represent?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Easy
A. An elbow-up or elbow-down posture
B. A second robot controller
C. A change in link material
D. A different battery voltage

13 What does DH stand for in robot kinematics?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Easy
A. Direct Horizontal
B. Digital Handling
C. Denavit-Hartenberg
D. Dynamic Height

14 What is the main purpose of DH parameters?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Easy
A. To describe link transformations
B. To select gripper material
C. To calculate battery charging time
D. To measure motor temperature

15 Which DH parameter represents rotation about the joint axis?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Easy
A. Link length
B. Twist angle
C. Joint angle
D. Link offset

16 Which DH parameter represents the distance along the common normal between two joint axes?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Easy
A. Link length
B. Twist angle
C. Joint angle
D. Link offset

17 In a planar two-revolute-joint robot, the joint axes are commonly parallel to which direction?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Easy
A. The vertical link direction
B. The axis perpendicular to the plane
C. The horizontal link direction
D. The direction toward the gripper

18 What should be done after calculating inverse kinematics angles?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Easy
A. Ignore the link dimensions
B. Remove the joint coordinate frames
C. Replace the target with a random point
D. Check the resulting end-effector position

19 In the Orangewood Robotic Arm laboratory, what do servo commands mainly control?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Easy
A. The computer screen brightness
B. The link manufacturing process
C. The room lighting level
D. The robot joint positions

20 Why must calculated angles be checked against the robot's joint limits?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Easy
A. The coordinate system loses its origin
B. The servos may not rotate through every angle
C. The links become mathematically weightless
D. The target position always changes color

21 For a two-link planar robot with link lengths cm and cm, which condition must a target point satisfy to be reachable?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Medium
A. only
B.
C.
D.

22 For a planar two-link arm, the geometric inverse-kinematics equation for the second joint angle is . What does changing the sign of represent?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Medium
A. A different elbow configuration
B. A different base position
C. A different target distance
D. A different link length

23 A target point for the Orangewood Robotic Arm has coordinates cm. What is the radial distance of the target from the robot base?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Medium
A. cm
B. cm
C. cm
D. cm

24 In the geometric solution for a two-axis planar articulated robot, which expression gives the first joint angle?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Medium
A.
B.
C.
D.

25 For cm and target cm, what is the value of ?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Medium
A.
B.
C.
D.

26 Using cm and target cm, the solution with gives approximately which value of ?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Medium
A.
B.
C.
D.

27 Why is preferred over in the inverse-kinematics program for the Orangewood Robotic Arm?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Medium
A. It avoids calculating the second joint
B. It determines the correct angular quadrant
C. It makes both links equal
D. It removes all joint limits

28 If the computed value of is for a target point, what is the most appropriate conclusion?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Medium
A. The target has two valid solutions
B. The target is outside the reachable workspace
C. The link lengths should be added twice
D. The first joint must rotate by

29 In the standard DH representation of a two-axis planar arm, which DH parameter normally represents the length of link along the common normal?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Medium
A.
B.
C.
D.

30 For a two-axis planar robot using standard DH parameters, what are the typical values of the link twists and ?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Medium
A. and
B. and
C. and
D. and

31 For a planar two-link arm with zero link offsets and zero link twists, which position equations result from the DH forward-kinematics model?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Medium
A. ,
B. ,
C. ,
D. ,

32 When comparing geometric and DH inverse-kinematics methods for the Orangewood Robotic Arm, what is a key advantage of the DH approach?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Medium
A. It provides a systematic frame-based model
B. It eliminates the need for coordinate frames
C. It always produces one joint solution
D. It applies only to arms with equal links

33 A two-link planar robot has cm and cm. Which target distance from the base lies exactly on its inner workspace boundary?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Medium
A. cm
B. cm
C. cm
D. cm

34 What happens to the two geometric inverse-kinematics solutions when the target lies at the maximum reach ?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Medium
A. They become perpendicular at
B. They disappear because is too large
C. They become identical at
D. They become identical at

35 A controller calculates joint angles in radians but sends servo commands using degrees. What error is most likely if no unit conversion is applied?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Medium
A. The arm rejects every reachable target
B. The arm interprets radian values as degree values
C. The arm automatically changes link lengths
D. The arm moves with the intended pose

36 For a target in the second quadrant, why can using produce an incorrect first joint angle?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Medium
A. The negative x-coordinate can shift the angle to the wrong quadrant
B. The ratio is always zero
C. The second joint angle becomes independent of the target
D. The ratio cannot represent link lengths

37 Which calculation is a useful verification after obtaining inverse-kinematics angles for the Orangewood Robotic Arm?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Medium
A. Multiply both angles by the link lengths
B. Set both joint angles to zero
C. Recompute using forward kinematics
D. Compare only the sign of

38 For a target located on the positive x-axis, , what does evaluate to when ?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Medium
A.
B.
C.
D.

39 In a DH-based inverse-kinematics implementation, why must the selected solution be checked against the Orangewood arm's joint limits?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Medium
A. A mathematically valid pose may exceed actuator limits
B. Joint limits determine the link lengths
C. Every mathematical solution is physically usable
D. Joint limits change the target coordinates

40 Which condition indicates a fully extended or folded singular configuration in a two-link planar robot?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Medium
A.
B.
C.
D.

41 A planar 2R Orangewood arm has and . Using the geometric inverse-kinematics model, which joint-angle pairs reach ?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Hard
A. or
B. or
C. or
D. or

42 For and , a target lies at radial distance from the base. What is the correct inverse-kinematics conclusion?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Hard
A. The target has two solutions because and
B. The target has one solution because it lies on the inner workspace boundary
C. The target is reachable only by choosing the positive square root for
D. The target is unreachable because and

43 A target is located at maximum extension, . Which statement best describes the inverse-kinematics solution and local behavior of the arm?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Hard
A. The elbow branches remain distinct at , and the Jacobian is full rank
B. The elbow branches remain distinct at , and the Jacobian is full rank
C. The elbow branches merge at , and the Jacobian loses rank
D. The elbow branches merge at , and the Jacobian loses rank

44 Using standard DH notation for a planar 2R arm with both revolute axes parallel to , which parameter table produces the conventional forward-kinematics equations?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Hard
A. and
B. and
C. and
D. and

45 Which ordered product of standard DH elementary transformations correctly represents one planar revolute link with parameters ?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Hard
A.
B.
C.
D.

46 A planar arm has and must reach . Using and expressing angles in , what are the two IK branches?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Hard
A. and
B. and
C. and
D. and

47 Suppose the physical DH angles satisfy , where is the Orangewood command and the calibrated offsets are and . If IK returns the physical solution , what commands should be sent?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Hard
A.
B.
C.
D.

48 For and , the desired end-effector pose is specified by , where . Which pose is exactly feasible?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Hard
A.
B.
C.
D.

49 For a target, geometric IK produces and . The Orangewood joint limits are and , with zero calibration offsets. Which result should the controller use?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Hard
A. Average the branches to obtain before commanding
B. Use because it is the only limit-feasible branch
C. Use because it has the smaller absolute first-joint angle
D. Reject both branches because their second-joint angles have opposite signs

50 An IK program computes for a joint, but the Orangewood API expects radians. If the numeric value is sent and the controller wraps angles into , what approximate physical angle results?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Hard
A.
B.
C.
D.

51 The robot base is located at in the world frame and rotated counterclockwise relative to it. For and , which joint configuration reaches the world target ?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Hard
A.
B.
C.
D.

52 An Orangewood planar arm has and a second link of . A rigid tool is mounted collinearly beyond link 2. Which joint pairs place the tool tip at ?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Hard
A. and
B. and
C. and
D. and

53 Due to floating-point error, an IK calculation returns for a target expected to lie on the outer workspace boundary. The solver tolerance is . What is the most appropriate action?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Hard
A. Declare the target unreachable because every value above is physically invalid
B. Clamp to , compute the folded solution, and verify joint limits
C. Clamp to , compute the boundary solution, and verify its FK residual
D. Replace by , compute both elbow branches, and compare joint norms

54 While following a smooth Cartesian path, independently selecting the principal-angle IK solution at each sample causes sudden joint jumps and occasional elbow switching. Which strategy best preserves a continuous Orangewood trajectory?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Hard
A. Wrap every angle independently and always select the positive value of
B. Average the elbow-up and elbow-down solutions before applying joint limits
C. Unwrap angles and select the feasible branch closest to the previous joint state
D. Select the branch with the smallest absolute at every sample

55 At and , which instantaneous Cartesian velocity cannot be generated by any finite joint-velocity vector for a standard planar 2R arm?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Hard
A. A tangential velocity produced by rotating both joints
B. A nonzero velocity purely along the base -axis
C. A zero velocity with nonzero null-space joint motion
D. A nonzero velocity purely along the base -axis

56 For , a candidate IK solution is . What pose should DH-based forward kinematics return?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Hard
A.
B.
C.
D.

57 With the base -axis pointing right and -axis pointing upward, how can the sign of an IK branch be identified geometrically from the first-link vector and second-link vector ?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Hard
A. A positive planar cross product corresponds to
B. A negative planar cross product corresponds to
C. A positive planar cross product corresponds to
D. A zero planar cross product corresponds only to

58 A planar arm has and . The requested target is , which is outside the workspace. If the controller minimizes Euclidean Cartesian error without considering joint limits, which configuration reaches the nearest attainable point?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Hard
A.
B.
C.
D.

59 For and , the target is , exactly on the inner workspace boundary. Which statement is correct?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Hard
A. Infinitely many solutions exist because every first-joint angle reaches the target
B. The target is unreachable because its radius is less than the longer link
C. Two distinct nonsingular branches exist at and
D. The branches coalesce physically at modulo

60 Which acceptance procedure is most robust when transferring computed IK solutions to an Orangewood arm with periodic revolute joints, calibration offsets, and finite joint limits?

Inverse kinematics of two-axis planar articulated robot using geometric approach and DH algorithm with Orangewood Robotic Arm Hard
A. Apply offsets, map equivalent angles into limits, and verify the target using forward kinematics
B. Clamp joint angles, ignore calibration offsets, and accept whenever
C. Round angles, ignore equivalent representations, and select the smallest absolute joint sum
D. Keep raw angles, enforce a fixed elbow branch, and skip Cartesian residual evaluation
Previous MCQ
Unit 4
Next MCQ
Unit 6