Soft continuum robots achieve complex deformation through elastic equilibrium, making their reachable motions governed jointly by structural design and actuation-induced mechanics. This work develops a general formulation that integrates equilibrium computation with kinematic performances by evaluating Riemannian Jacobian spectra on the equilibrium manifold shaped by internal/external loading. The resulting framework yields a global performance functional that directly links structural parameters, actuation inputs, and the induced configuration space geometry. We apply this general framework to magnetic actuation. Analytical characterization is obtained under weak uniform fields, revealing optimal placement and orientation of the embedded magnet with invariant scale properties. To address nonlinear deformation and spatially varying fields, a two-level optimization algorithm is developed that alternates between energy based equilibrium search and gradient based structural updates. Simulations and physical experiments across uniform field, dipole field, and multi-magnet configurations demonstrate consistent structural tendencies: aligned moments favor distal or mid-distal solutions through constructive torque amplification, whereas opposing moments compress optimal designs toward proximal regions due to intrinsic cancellation zones.

翻译：软体连续体机器人通过弹性平衡实现复杂形变，其可达运动由结构设计与致动诱导力学共同决定。本研究发展了一种通用框架，通过评估由内/外载荷塑造的平衡流形上的黎曼雅可比谱，将平衡计算与运动学性能相集成。所得框架产生了一个全局性能泛函，直接关联结构参数、致动输入及诱导构型空间几何。我们将此通用框架应用于磁致动场景。在弱均匀磁场下获得解析表征，揭示了嵌入磁体具有不变尺度特性的最优位置与取向。针对非线性形变与空间变化磁场，开发了一种双层优化算法，交替进行基于能量的平衡搜索与基于梯度的结构更新。在均匀场、偶极场及多磁体配置下的仿真与物理实验均显示一致的结构趋势：同向磁矩通过建设性扭矩放大倾向于远端或中远端解，而反向磁矩则因固有抵消区域将最优设计压缩至近端区域。