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°?
What is the DH parameter that represents the distance between axes Zi-1 and Zi along Xi-1?
What is the significance of the last column in a homogeneous transformation matrix?
What is the angle measured by in the problem given?
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What is the DH parameter that represents the angle between Xi-1 and Xi about Zi?
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What is the formula for calculating the radius of the inner circle in the 2R chain workspace?
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How many possible solutions are there for inverse kinematics in a 2R planar serial manipulator?
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What do the upper-left 3x3 elements typically represent in a 4x4 homogeneous transformation matrix for a 3D transformation?
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What is the mobility of a kinematic chain having 4 joints and 5 links?
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What is the shape of the workspace of a 2R serial manipulator?
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What is the correct Jacobian Matrix for a 2R serial manipulator?
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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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Description
Test your understanding of robotics and kinematics concepts, including calculation of radius, mobility of kinematic chains, and workspace of serial manipulators. Evaluate your knowledge of inverse kinematics and more.
