由不相容力矩評估建立之具有彈簧與馬達的複合式重力平衡方法

Abstract

靜平衡對於串聯式機械臂維持其靜態姿態至關重要。當前大多數機械臂使用馬達達成靜態平衡，由於機械臂關節累積了其所有後接桿件的重力影響，此方法需要使用具有高峰值扭矩的馬達。根據先前研究，接地彈簧也可以實現靜態平衡。然而，此方法中必要的高跨接的接地彈簧除了平衡重力扭矩之外，還會產生不匹配重力扭矩的扭矩，需要額外的彈簧來抵消。 為了減少對高跨接彈簧的需求，我們引入馬達平衡需要高跨接彈簧的重力扭矩。配置參數被定義為最高跨接彈簧的限制，該參數確定了馬達扭矩需求，進一步決定了複合式重力平衡的配置。 我們用兩個指標來評估複合式重力平衡的配置的優劣。第一個是與彈簧扭矩不相容的重力扭矩，也就是配置中的所需馬達扭矩；第二個是與重力扭矩不相容的彈簧非重力平衡扭矩。我們將這兩個指標的加權總和定義為不相容扭矩的總和，並尋求具有最小不相容扭矩總和的複合式重力平衡的配置。通過利用與重力扭矩相比較小的補充馬達扭矩，整體彈簧配置可以具有更高比例的重力平衡扭矩，因此複合式重力平衡方法更加有效率。 本文以三自由度的複合式重力平衡串聯型機械臂作為說明範例。與僅使用彈簧相比，複合式重力平衡方法可以將非重力平衡扭矩貢獻降低27.11%。與僅使用馬達相比，能夠將馬達峰值扭矩降低91.01%。

Static balancing is essential for a serial-connected manipulator to maintain its static posture. Most manipulators nowadays use motors for static balancing, necessitating motors with high peak torque as the joint further away from the end link cumulates more gravitational torque contribution from all of its succeeding links. Previous studies showed that ground-attached high-spanning springs can also achieve static balancing. However, besides gravity-balancing torque, these springs also bring torque contributions that do not match the gravitational torque, requiring extra springs to counter. To reduce the requirement of high-spanning springs, motor torque is introduced only to balance the gravitational torque that requires high-spanning springs. The arrangement parameter is defined as the boundary for the highest spanning spring which determines the motor torque requirement and further determines the hybrid configuration. Two indicators are chosen to evaluate the quality of a hybrid configuration. The first is the gravitational torque which is incompatible with the spring torque, i.e., the required motor torque. The second is the spring torque which is incompatible with the gravitational torque, i.e., the non-gravity-balancing torque of the springs. We define the weighted sum of these two indicators as the sum of incompatible torque and seek the hybrid configuration with a minimum sum of incompatible torque. we can use complementary motor torque and spring configuration with a lower ratio of non-gravity-balancing torque contribution to obtain hybrid gravity balancing which is considered more efficient. An illustrative example of a 3-DOF manipulator that employs the hybrid balancing technique is presented. It is shown that the hybrid balancing method can decrease the non-gravity-balancing torque contribution by 27.11% compared to using only springs and reduces motor peak torque by 91.01% compared to using only motors.