為了實現精準且效率的運動表現，並避免過大的加減速變化影響系統動態行為，甚至造成機台受損，本文考量 3-UPU 機構之三軸長度變化急跳度與馬達驅動扭矩，規劃出運動輪廓最佳化之方法。
本文首先在工作空間(Work space)中，規劃末端效應器之 S 型(Sigmoid-Curve)運動曲線，完成初步的速度規劃。而後推導機構之順、逆向運動學解析解，求得系統線性驅動量與末端效應器座標之關係。再以逆向運動學推導出之關節空間中(Joint space)，連桿長度變化的運動輪廓，考慮其加速度和急跳度限制，將時間視為變量並以最小化總運動時間為目標，以 MATLAB 之 fmincon 函式進行非線性約束之速度曲線最佳化。同時，利用逆向動力學可推導驅動軸之線性推力和扭矩，並利用驅動扭矩計算系統的能耗，將能耗納入連桿長度變化曲線優化的限制條件之一，確保在平滑過程中不會導致過高的能源消耗。
同時，為了驗證運動精度與能耗要求，本文建立了包含滾珠螺桿撓性影響的 Simulink 機構模型，以模擬系統的動態響應。最終，本文提出的方法能有效降低機構振動，並在能耗控制方面滿足合理範圍，充分發揮並聯式工具機的性能。

To achieve precise and efficient motion performance, and to avoid sudden changes in acceleration and deceleration that could impact the dynamic behavior of the system or even cause damage to the machine, this paper considers the jerk of change of link length and the motor torque for optimizing the motion profile.
First, in the workspace, the end-effector’s motion profile is designed by Sigmoid-Curve to complete the initial velocity planning of the mechanism. Subsequently, the forward and inverse kinematic analytical solutions are derived to establish the relationship between the link length and the coordinate of end-effector. Then using the inverse kinematic derives the accelerations and jerks of change of link length as constraints, this paper adopts time as a variable and performs the nonlinear constraint optimization of the velocity curve, with the objective of minimizing the total motion time by MATLAB’s fmincon function.
Simultaneously, to verify the motion accuracy and energy consumption, a Simulink model of the mechanism, incorporating the flexibility of ball screws, is established to simulate the system’s dynamic response. The inverse dynamics are also used to derive the linear thrust and the motor torque of drive shafts. The energy consumption of the system is calculated based on the driving torque, ensuring that the smoothing process will not result in excessive energy consumption. Ultimately, the proposed method effectively reduces the mechanism’s vibration and meets reasonable energy consumption requirements, thereby fully exploiting the performance of the parallel kinematic machine tool.

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