The H-frame (also known as H-Bot) architecture is a simple and elegant two-axis parallel positioning system used to construct the XY stage of 3D printers. It holds potential for high speed and high dynamic performance due to the use of frame-mounted motors that reduce the moving mass of the printer while allowing for the use of (heavy) higher torque motors. However, the H-frame’s dynamic accuracy is limited during high-acceleration and high-speed motion due to racking – i.e., parasitic torsional motions of the printer’s gantry due to a force couple. Mechanical solutions to the racking problem are either costly or detract from the simplicity of the H-frame. In this paper, we introduce a feedforward software compensation algorithm, based on the filtered B-splines (FBS) method, that rectifies errors due to racking. The FBS approach expresses the motion command to the machine as a linear combination of B-splines. The B-splines are filtered through an identified model of the machine dynamics and the control points of the B-spline based motion command are optimized such that the tracking error is minimized. To compensate racking using the FBS algorithm, an accurate frequency response function of the racking motion is obtained and coupled to the H-frame’s and $\mathit{y}$-axis dynamics with a kinematic model. The result is a coupled linear parameter varying model of the H-frame that is utilized in the FBS framework to compensate racking. An approximation of the proposed racking compensation algorithm, that decouples the $\mathit{x}$- and $\mathit{y}$-axis compensation, is developed to significantly improve its computational efficiency with almost no loss of compensation accuracy. Experiments on an H-frame 3D printer demonstrate a 43% improvement in the shape accuracy of a printed part using the proposed algorithm compared to the standard FBS approach without racking compensation. The proposed racking compensation algorithm can be used in-conjunction with mechanical solutions, or as a stand-alone solution, to improve the performance of H-frame architectures.

H-frame（也称为 H-Bot）架构是一种简单而优雅的两轴平行定位系统，用于构建 3D 打印机的 XY 平台。由于使用安装在框架上的电机减少了打印机的移动质量，同时允许使用（重型）更高扭矩的电机，因此它具有高速和高动态性能的潜力。然而，H 框架的动态精度在高加速度和高速运动期间由于齿条而受到限制 - 即由于力偶引起的打印机机架的寄生扭转运动。货架问题的机械解决方案要么成本高，要么有损 H 型框架的简单性。在本文中，我们介绍了一种基于滤波 B 样条 (FBS) 方法的前馈软件补偿算法，该算法可纠正因机架引起的错误。FBS 方法将机器的运动命令表示为 B 样条的线性组合。通过识别的机器动力学模型过滤 B 样条，并优化基于 B 样条的运动命令的控制点，从而使跟踪误差最小化。为了使用 FBS 算法补偿摇摆，摇摆运动的准确频率响应函数被获得并耦合到 H 框架的和$\mathit{是}$- 带有运动学模型的轴动力学。结果是在 FBS 框架中使用的 H 框架的耦合线性参数变化模型来补偿货架。提出的机架补偿算法的近似值，它解耦了$\mathit{X}$- 和 $\mathit{是}$轴补偿，旨在显着提高其计算效率，而几乎不会损失补偿精度。在 H 型框架 3D 打印机上的实验表明，与没有机架补偿的标准 FBS 方法相比，使用所提出的算法打印部件的形状精度提高了 43%。提出的机架补偿算法可与机械解决方案结合使用，或作为独立解决方案使用，以提高 H 框架架构的性能。