2D Mechanical Linkage Designer

Original prompt

Build an interactive 2D mechanical linkage designer.

Users should be able to:
- create fixed pivots
- create rotating joints
- create rigid links with exact lengths
- create sliders constrained to tracks
- connect components into mechanisms
- choose a driving joint or motor
- play, pause, reset, and step the simulation
- display joint coordinates and link lengths
- save and reload mechanisms

Support at least:
- a four-bar linkage
- a crank-slider mechanism

Rigid links must preserve their lengths throughout the simulation, and constrained joints must remain attached.

Chinese translation

构建一个交互式二维机械连杆设计器。用户可以创建固定转轴、旋转关节、具有精确长度的刚性杆件、受轨道约束的滑块，并将它们连接为机械机构；可选择驱动关节或电机，支持播放、暂停、重置、单步，显示关节坐标与杆长，并保存/加载机构。至少应支持四连杆机构和曲柄滑块机构。整个模拟过程中刚性杆长度必须保持不变，受约束关节不能脱离连接。

Expected outcome

The deliverable should be a geometric-constraint-based mechanism simulator rather than a frame-by-frame decorative animation. Link lengths, pivots, and slider tracks should remain continuously constrained while a driven joint causes the rest of the mechanism to solve accordingly. Four-bar and crank-slider mechanisms should move stably and expose useful measurements and joint trajectories.

Additional verification guidance

• Sample rigid-link lengths throughout the motion cycle and confirm errors remain within a reasonable tolerance.
• Run four-bar and crank-slider mechanisms and verify that joints remain attached and sliders stay on their tracks.
• Pause and step the mechanism, confirming step results match continuous simulation at equivalent states.
• Save and reload mechanisms and verify geometry, connections, drive settings, and dimensions restore completely.