Robotics and Kinematics Quiz

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.