Robotics and Kinematics Quiz

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Questions and Answers

What is the value of x-coordinate of the tool tip of a 2R serial manipulator given l1 = 10 cm, l2 = 25 cm, θ1 = 45° and θ2 = 30°?

  • 13.54 cm
  • 28.72 cm (correct)
  • 19.57 cm
  • 31.22 cm

What is the DH parameter that represents the distance between axes Zi-1 and Zi along Xi-1?

  • Joint Offset d
  • Joint Angle θ
  • Link twist angle α
  • Link Length a (correct)

What is the significance of the last column in a homogeneous transformation matrix?

  • Link length
  • Shear factors
  • Position vector (correct)
  • Rotation angles

What is the angle measured by in the problem given?

<p>Angle between Zi-1 and Zi about Xi-1 (B)</p> Signup and view all the answers

What is the DH parameter that represents the angle between Xi-1 and Xi about Zi?

<p>Joint Angle θ (B)</p> Signup and view all the answers

What is the formula for calculating the radius of the inner circle in the 2R chain workspace?

<p>|l1 – l2 | (A)</p> Signup and view all the answers

How many possible solutions are there for inverse kinematics in a 2R planar serial manipulator?

<p>One or two solutions (C)</p> Signup and view all the answers

What do the upper-left 3x3 elements typically represent in a 4x4 homogeneous transformation matrix for a 3D transformation?

<p>Rotation matrix (D)</p> Signup and view all the answers

What is the mobility of a kinematic chain having 4 joints and 5 links?

<p>2 (B)</p> Signup and view all the answers

What is the shape of the workspace of a 2R serial manipulator?

<p>The region between 2 concentric circles (B)</p> Signup and view all the answers

What is the correct Jacobian Matrix for a 2R serial manipulator?

<p>𝐽 = − 𝑙 1 𝑠 1 − 𝑙 2 𝑠 12 − 𝑙 2 𝑠 12 𝑙 1 𝑐 1 + 𝑙 2 𝑐 12 𝑙 2 𝑐 12 [ ] (A)</p> Signup and view all the answers

Flashcards

Link Length 'a'

The distance between the axes Zi-1 and Zi measured parallel to the Xi-1 axis.

Joint Angle 'θ'

The angle between the axes Xi-1 and Xi measured about the Zi axis.

Position Vector

The last column of a homogeneous transformation matrix represents the position of the frame relative to the previous frame.

Inner Circle Radius

The radius of the smaller circle in the workspace of a 2R serial manipulator is equal to the absolute difference between the lengths of the two links.

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Mobility

The number of independent motions that a robot can make.

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Workspace of a 2R Manipulator

The workspace of a 2R serial manipulator is the area that the end effector can reach.

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Jacobian Matrix

A matrix that relates the joint velocities to the end effector velocity in a robot.

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Rotation Matrix

The upper-left 3x3 elements of a 4x4 homogeneous transformation matrix for a 3D transformation represent the rotation of the frame.

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Mobility of a 4-joint, 5-link chain

A kinematic chain with 4 joints and 5 links has 2 degrees of freedom, meaning it can move in two independent ways.

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Inverse Kinematics Solutions

For a 2R planar manipulator, there can be one or two possible solutions for the joint angles that result in the same end effector position.

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X-coordinate of the tool tip

The x-coordinate of the tool tip of a 2R serial manipulator is determined by the lengths of the links and the joint angles.

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Study Notes

2R Serial Manipulator

  • A 2R serial manipulator has l1 = 10 cm, l2 = 25 cm, θ1 = 45°, and θ2 = 30°.
  • The position of the tool tip can be calculated using these values.
  • The correct answer for the position of the tool tip is x = 28.72 cm, y = 19.57 cm.

DH Parameters

  • Link twist angle α is the angle between Z^(i-1) and Z^i about X^(i-1).
  • Link length a is the distance between Z^(i-1) and Z^i along X^(i-1).
  • Joint offset d is the distance between X^(i-1) and X^i along Z^i.
  • Joint angle θ is the angle between X^(i-1) and X^i about Z^i.

Homogeneous Transformation Matrix

  • The last column in a homogeneous transformation matrix represents the position vector.

Workspace of 2R Serial Manipulator

  • The radius of the inner circle in the 2R chain workspace is calculated as |l1 – l2|/2.
  • The workspace of a 2R serial manipulator is the region between two concentric circles.

Kinematic Chain

  • The mobility (m) of a kinematic chain having 4 joints and 5 links is 1.

Inverse Kinematics

  • Inverse kinematics for a 2R planar serial manipulator will yield one or two solutions.

Jacobian Matrix

  • The correct Jacobian Matrix for a 2R serial manipulator is 𝐽 = [− 𝑙 1 𝑠 1 − 𝑙 2 𝑠 12, 𝑙 1 𝑐 1 + 𝑙 2 𝑐 12; − 𝑙 2 𝑠 12, 𝑙 2 𝑐 12].

Forward Kinematics

  • Forward kinematics for a 3-link planar chain will yield one or two solutions.

Homogeneous Transformation Matrix (again)

  • In a 4x4 homogeneous transformation matrix for a 3D transformation, the upper-left 3x3 elements typically represent a rotation matrix.

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