Task-Distribution-Aware Counterweight Synthesis and Constrained Co-Design for Serial Manipulators

תקציר מקורי באנגליתarXiv:2609.15082v1 Announce Type: cross 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 $m_c=p/r_c$,