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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°?
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 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 significance of the last column in a homogeneous transformation matrix?
What is the angle measured by in the problem given?
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?
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?
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?
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?
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?
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?
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?
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.
