Vertex range of motion of a two-degree-of-freedom robotic arm

For a two-degree-of-freedom robotic arm, the range of motion of its vertex refers to the spatial range that the arm can reach, which is usually represented by a planar region. In a two-degree-of-freedom robotic arm, the first degree of freedom is the angle of base rotation, and the second degree of freedom is the length of the arm, so the range of motion of the arm's vertex is a two-dimensional planar region.

Specifically, the range of vertex motion of a two-degree-of-freedom robotic arm depends on the constraints of its two degrees of freedom. For example, if the rotation angle of the first degree of freedom ranges from [0, 2π) and the length of the second degree of freedom ranges from [0, l], the range of motion of the vertex of the robotic arm is a circular region with radius l and the center of the circle is located at the center of the base.

If the rotation angle range of the first degree of freedom is [-π/2, π/2] and the length range of the second degree of freedom is [0, l], the vertex motion range of the robotic arm is a sector area, the center angle of the sector is π, the center of the circle is located in the center of the base, and the radius is l.

In the vertex motion range of the robotic arm, there also exists some special positions, such as the robotic arm s maximum span point and maximum radius point. The maximum span point refers to the farthest distance that the arm can span, and the maximum radius point refers to the farthest radius position that the arm can reach. These special positions are important for the motion control and path planning of the robotic arm.

In summary, the range of motion of the vertex of a two-degree-of-freedom robotic arm is a two-dimensional planar region that depends on the constraints of its two degrees of freedom and is important for the control and planning of the robotic arm.