隨著人型機器人技術蓬勃發展，手指關節傳動元件之微型化需求日益迫切。傳統定導程滾珠螺桿之輸出速度與輸入轉速呈固定線性比例，若欲實現非線性速度輸出，須仰賴控制器即時調速，導致驅動系統架構複雜，不利微型化應用。本研究提出以速度曲線為核心之微型變導程螺桿設計方法，運用Mathematica由目標速度曲線反推局部導程分布，建立速度創成方法，生成螺旋線幾何座標，並針對圓弧、五段梯形及七段S-curve三種工況完成設計計算。本機構依驅動元件與旋轉拘束對象配置之差異，可彈性配置為三種運動方式，分別對應機器人手指關節、SCARA機器手臂與線性致動器等應用場景，本研究以手指關節之運動方式為對象進行後續建模與模擬驗證。溝槽截面幾何採哥德式溝槽，依接觸角與螺桿直徑等約束求解圓弧半徑與圓心偏移量，確保滾珠與溝槽保持四點接觸。完成三維建模後，以RecurDyn建立多體動力學(Multi-Body Dynamics， MBD)模型，模擬採赫茲接觸理論建立非線性接觸模型。結果顯示，三種工況之軸向速度與位移曲線均與理論設計高度吻合，平均位移誤差均控制在1%以內，驗證以速度曲線所建立之幾何設計流程具備良好準確性。此外，本研究針對有背隙與消除背隙兩種模型配置進行遲滯迴圈曲線比對，結果顯示消除背隙設計可使螺帽輸入轉角反轉處之位移遲滯量降低約19.9%，驗證定位螺絲預壓機構對抑制背隙遲滯行為之有效性。本研究亦針對滾珠接觸力峰值、位能循環行為，以及驅動能量與磨耗傾向指標進行交叉比較，結果顯示速度曲線平順程度為影響接觸力波動與磨耗傾向之關鍵因素，可作為後續機構優化與潤滑對策之參考，並為變導程螺桿應用於人形機器人手指關節致動提供設計基礎。;With the rapid development of humanoid robotics， the demand for miniaturized finger joint transmission components has become increasingly critical. In conventional constant-lead ball screws， the axial output velocity is linearly proportional to the input rotational speed. Achieving nonlinear velocity output therefore requires real-time motor speed regulation through an external controller， which increases the complexity of the drive architecture and is unfavorable for miniaturized applications. This study proposes a miniature variable-lead screw design method centered on velocity profile planning. Mathematica is employed to inversely derive the local lead distribution from a target velocity curve， establishing a velocity generation method and generating the corresponding helix coordinate data. Design calculations are completed for three operating conditions: circular-arc， five-segment trapezoidal， and seven-segment S-curve profiles. Depending on the assignment of the driving component and the rotational constraint， the mechanism can be flexibly configured into three motion modes， corresponding respectively to humanoid finger-joint actuation， SCARA robotic arm end-joints， and linear-actuator applications; the finger-joint motion mode is adopted for the subsequent modeling and simulation validation in this study. The groove cross-section adopts a Gothic arch geometry， with the arc radius and center offset solved numerically under geometric constraints of contact angle and screw diameter， ensuring that the balls maintain four-point contact with the groove. Following three-dimensional modeling， a multibody dynamics (MBD) model is established in RecurDyn， in which a nonlinear contact model based on Hertzian contact theory is adopted throughout the simulation. Results show that the axial velocity and displacement curves of all three conditions agree well with the theoretical design， with average displacement errors kept within 1%， confirming the accuracy of the geometric design procedure established through velocity profile planning. In addition， a comparison of the backlash hysteresis loops between configurations with and without backlash elimination shows that the anti-backlash design reduces the displacement hysteresis at input-direction reversal of the nut by approximately 19.9%， confirming the effectiveness of the preload-adjustment mechanism via the set screws in suppressing backlash hysteresis. This study further conducts a cross-comparison of ball contact force peaks， potential-energy cycling behavior， and driving input energy together with a wear-tendency index across the three conditions. The results indicate that the smoothness of the velocity profile is the key factor governing contact force fluctuation and wear tendency， providing a reference for future mechanism optimization and lubrication strategy， as well as a design foundation for applying the variable-lead screw to humanoid robot finger joint actuation.
