Fig 1.
An abstract diagram of the human-pole-load system.
Two loads are attached to the pole and the pole interfaces with the human at the shoulder and hands. Some attributes of each component are also listed.
Fig 2.
A typical pole carriage diagram.
The pole is carried in the frontal style and the right hand controls the pole balance. Two loads are suspended with ropes at each end of the pole. The pole deforms due to the load weights.
Fig 3.
Four abstract types of the carrying pole.
(A) NSNR (no spring, no rope); (B) WSNR (with spring, no rope); (C) NSWR (no spring, with rope); (D) WSWR (with spring, with rope).
Fig 4.
The model of the human-pole-load system.
The free body diagram of the system and the diagram of the contact model that contains two spring-damping units.
Fig 5.
Balance control of the carrying pole.
(A) The closed-loop control system depicting the pole carriage scenario. (B) The trajectory of the shoulder in horizontal (xo) and vertical direction (yo) for testing the step response of the pole model.
Fig 6.
Rollover angle variation without hand control at different conditions.
(A) Simulated using the NSNR model with different tangential stiffness values where khs = 10000N/m, L = 1.4m. (B) Simulated using the NSNR model with different vertical stiffness values where kds = 500N/m, L = 1.4m. (C) Simulated using the NSNR model with different pole length values where kds = 500N/m,khs = 10000N/m (D) Simulated using the WSNR model with different pole stiffness values where kds = 500N/m, khs = 10000N/m,L = 1.4m. (E) Simulated using the NSWR model with different rope length values where kds = 500N/m,khs = 10000N/m,L = 1.4m.
Fig 7.
A PD controller can stabilize the NSNR model, keeping the pole angle around zero.
The maximal angle θmax and settling time ts are also defined, as depicted, for comparison in later simulations.
Fig 8.
Rollover angle variation with step input and active control under different conditions.
(A) Simulated using the NSNR model with different pole lengths, where kds = 500N/m, khs = 10000N/m (B) Simulated using the WSNR model with different pole stiffness, where kds = 500N/m, khs = 10000N/m,L = 1.4m. (C) Simulated using the NSWR model with different rope lengths, where kds = 500N/m, khs = 10000N/m,L = 1.4m. The max angle and settling time are also compared in bar graphs and the color of each bar corresponds to the waveform color.
Fig 9.
Influence of pole length on the balance of the pole and pole-carrier interaction.
Simulated using the NSNR model with two pole length values (blue: L = 1.4m and red: L = 1.8m) and kds = 500N/m, khs = 10000N/m. Simulation results for: (A) the pole angle, (B) control force at the hand, and the interaction force at the shoulder in (C) forward direction and (D) vertical direction.
Fig 10.
Influence of pole stiffness on the balance of the pole and pole-carrier interaction.
Simulation of the rigid condition (in blue, using the NSNR model and L = 1.4m, kds = 500N/m, khs = 10000N/m) and low stiffness condition k1,2 = 500N/m (in red, using the WSNR model and L = 1.4m, kds = 500N/m, khs = 10000N/m). Simulation results for: (A) the pole angle, (B) control force at the hand, and the interaction force at the shoulder in (C) forward direction and (D) vertical direction are shown.
Fig 11.
Influence of rope on the balance of the pole and pole-carrier interaction.
The no rope condition (in blue, using the NSNR model and L = 1.4m, kds = 500N/m, khs = 10000N/m) and the condition with a rope length of 1m (in red, using the NSWR model and L = 1.4m, kds = 500N/m, khs = 10000N/m) are shown. Simulation results for: (A) the pole angle, (B) control force at the hand, and the interaction force at the shoulder in (C) forward direction and (D) vertical direction are shown.
Fig 12.
The combined influence of pole stiffness and rope on pole balance and pole-carrier interaction.
The comparison is made between the condition of no spring and no rope (in blue, using the NSNR model and L = 1.4m, kds = 500N/m, khs = 10000N/m) and the condition of pole stiffness k1,2 = 500 N/m and rope length Lr1,2 = 1m (in red, using the WSWR model and L = 1.4m, kds = 500N/m, khs = 10000N/m). Simulation results for: (A) the pole angle, (B) control force at the hand, and the interaction force at the shoulder in (C) forward direction and (D) vertical direction are shown.
Fig 13.
The combined influence of pole stiffness and rope on pole balance and pole-carrier interaction.
The comparison is made between the condition of no spring and no rope (in blue, using the NSNR model and L = 1.4m, kds = 4000N/m, khs = 10000N/m) and the condition of pole stiffness k1,2 = 500 N/m and rope length Lr1,2 = 1m (in red, using the NSNR model and L = 1.4m, kds = 4000N/m, khs = 10000N/m). Simulation results for: (A) the pole angle, (B) control force at the hand, and the interaction force at the shoulder in (C) forward direction and (D) vertical direction are shown.