Design, Dynamics, and Workspace of a Hybrid-Driven-Based Cable Parallel Manipulator

Algorithm 1

Flowchart of generating the workspace of the HDCPM.

     𝑥^′_min=−𝑙^′₁+𝑙^′₂,𝑥^′_max=𝑙^′₃+𝑙^′₄+𝑙^′₅

𝑧^′_min=−max𝑙^′₁+𝑙^′₂,𝑙^′₃+𝑙^′₄,𝑧^′_max=max𝑙^′₁+𝑙^′₂,𝑙^′₃+𝑙^′₄

𝑥^′=𝑥^′_min,𝑧^′=𝑧^′_min

Do While  𝑧^′≤𝑧^′_max

     Do While  𝑥^′≤𝑥^′_max

          If  𝑙^′₁−𝑙^′₂<𝐿_𝐴𝐶<𝑙^′₁+𝑙^′₂and𝑙^′₃−𝑙^′₄<𝐿_𝐶𝐸<𝑙^′₃+𝑙^′₄  Then

           From 𝑙₁=𝑠−𝑝+𝑙^′₅−𝑥^′_𝐶²+ℎ−𝑧^′_𝐶²,𝑙₁ is determined.

           Similarly, 𝑙₂,𝑙₃, and 𝑙₄ can be calculated, respectively.

           Record 𝑙_𝑖

          End If

       𝑥^′=𝑥^′+Δ𝑥^′

      Loop

       𝑧^′=𝑧^′+Δ𝑧^′

Loop

Various combinations of 𝑙_𝑖 for calculating coordinates (𝑥,𝑦,𝑧) by

𝑥=𝑙²₁−𝑙²₂+𝑎²/2𝑎,𝑦=𝑙²₁−𝑙²₄+𝑏²/2𝑏,𝑧=ℎ−𝑙²₁−𝑥²−𝑦²

and those satisfying motion range of the end-effector (0<𝑥<𝑎,0<𝑦<𝑏,0<𝑧<ℎ)

and tension condition (𝑇_𝑖>0) will generate the workspace