Task-Distribution-Aware Counterweight Synthesis and Constrained Co-Design for Serial Manipulators
arXiv:2609.15082v1 Announce Type: new Abstract: Passive counterweights are simple gravity compensators, but a counterweight selected from a single pose is not generally optimal for the configurations and tasks a manipulator actually executes. This paper develops a task-distribution-aware synthesis framework in which the operating distribution $\rho(q)$ enters the design explicitly. For a counterweight moment $p=m_c r_c$ with gravity torque $-gp\phi(q)$, the weighted mean-square residual gravity
Overview
arXiv:2609.15082v1 Announce Type: new Abstract: Passive counterweights are simple gravity compensators, but a counterweight selected from a single pose is not generally optimal for the configurations and tasks a manipulator actually executes. This paper develops a task-distribution-aware synthesis framework in which the operating distribution $\rho(q)$ enters the design explicitly. For a counterweight moment $p=m_c r_c$ with gravity torque $-gp\phi(q)$, the weighted mean-square residual gravity torque has the closed-form minimizer $p^*=E_\rho[\tau_g\phi]/(gE_\rho[\phi^2])$. If payload gravity torque is affine in payload mass, the optimum is also affine: $p^*(m_p,\rho)=p_0^*(\rho)+m_pK_p(\rho)$. For fixed static moment, added counterweight inertia is $I_c=pr_c$ while mass is $m_c=p/r_c$, so mass-radius selection is underdetermined unless physical constraints are specified. A recovered three-link manipulator is used as a case study. At $r_c=0.20$ m, zero-payload equivalent optima are 0.672 kg for uniform joint-space operation, 0.683 kg for approximately uniform task-space operation, 0.713 kg for a representative pick-and-place family, and 0.952 kg for a high-gravity-biased distribution, a change of more than 40% caused solely by the operating distribution. Nondominated fronts show that preferred mass-radius pairs depend on declared engineering bounds. A rated-torque-referenced all-joint screen increases zero-payload feasible task-space coverage from 78.1% without compensation to 93.7% for the uniform-distribution design. A lumped point-mass trajectory study gives a provisional crossover from no counterweight at very aggressive motion to stronger compensation as motion slows. These actuator and dynamic results are engineering consequence studies rather than physical validation.
Source
Originally published at arxiv.org.
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Source: https://arxiv.org/abs/2609.15082