Execute a GeoGebra command. To make a mechanism MOVE (animate), you MUST create an angle slider and define points that depend on it.

── COMMAND REFERENCE ──

POINTS: A = (x, y) — free point A = (3, 4) M = Midpoint(A, B) — midpoint P = Point(c, 0.5) — point on curve c at parameter 0..1

ANGLE SLIDER (the KEY to animation): α = 30° — creates an angle slider. ALWAYS start with this β = 60° — for mechanisms needing a second angle These become sliders. Use StartAnimation(α) to drive motion.

DEPENDENT POINTS (formulas using the angle): A = O1 + (rcos(α), rsin(α)) A = (rcos(α), rsin(α)) — same when O1 is origin X = (acos(α), bsin(α)) — ellipse motion These points MOVE when α changes. This is how animation works.

LINES & SEGMENTS: Line(A, B) — infinite line through A,B Segment(A, B) — segment between A,B Ray(A, B) — ray from A through B PerpendicularLine(A, l)— line through A ⟂ l ParallelLine(A, l) — line through A ∥ l

CIRCLES & ARCS: Circle(O, r) — circle center O radius r Circle(O, A) — circle center O through point A c = Circle(O1, 2) — name it 'c' to reuse

INTERSECTIONS (critical for mechanisms): P = Intersect(c1, c2) — all intersections P = Intersect(c1, c2, 1) — FIRST intersection (use 1 or 2) P = Intersect(c1, c2, 2) — SECOND intersection P = Intersect(Segment(A,B), c) — segment-circle intersection

ANGLES: Angle(A, O, B) — ∠AOB in degrees

SLIDER (numeric): r = 2 — creates a numeric slider if value is a plain number r = Slider(0, 5, 0.1) — explicit slider(min, max, step)

TRANSFORMATIONS: Rotate(A, α, O) — rotate A around O by angle α Dilate(A, s, O) — dilate A from O by factor s Translate(A, v) — translate A by vector v

ANIMATION: StartAnimation(α) — start the slider α animating StartAnimation() — start all sliders StopAnimation() — stop all animations SetAnimationSpeed(α, s) — set speed (0.1–10) After building the mechanism, always call StartAnimation(angle_label) and then geogebra_animate() for speed control.

MISC: ZoomIn(1) — zoom ZoomOut(1) — un-zoom Pan(x, y) — pan view

── CRITICAL RULES ──

1. ALWAYS create an angle slider (eg α=30°) FIRST before dependent points

2. Dependent points use cos(α), sin(α) — they move when α animates

3. For linkages, define fixed pivots → slider → dependent points → segments

4. Intersect() with index 1 or 2 picks WHICH intersection to use

5. After all commands, call geogebra_animate() to start motion

Args: command: GeoGebra command string (see reference above)

在 GeoGebra 中批量执行多条命令。适合一次性构建完整机构。

Args: commands_json: JSON 数组格式的命令列表, 如 '["A=(0,0)","B=(6,0)","Segment(A,B)"]'

Execute multiple GeoGebra commands from a structured list. Preferred over geogebra_batch for AI clients — no JSON string wrapping needed.

Args: commands: Ordered GeoGebra commands, e.g. ["A=(0,0)", "B=(6,0)", "Segment(A,B)"]

新建空白 GeoGebra 构造，清除当前所有对象。

保存当前 GeoGebra 构造为 .ggb 文件。

Args: filepath: 保存路径, 如 "D:/tool/my_mechanism.ggb"

导出当前 GeoGebra 视图为 PNG 截图。

Args: filepath: 保存路径, 如 "D:/tool/screenshot.png" scale: 缩放因子 (1-4, 默认2)

返回 MCP Server 版本号。

获取 GeoGebra 命令和机构设计的帮助。在构建机构之前先调用此工具。

Args: topic: "commands"=命令参考, "mechanisms"=机构模板, "animation"=动画, "all"=全部

检查 GeoGebra 连接状态和当前构造信息。

设置 GeoGebra 视图模式。

Args: perspective: "G"=几何, "A"=代数, "T"=表格, "3D"=三维, "AG"=代数+几何

设置对象外观（颜色、线宽、点大小、可见性）。

Args: label: 对象标签名 color_r/g/b: RGB 颜色 0-1 (-1 不修改) thickness: 线宽 1-13 point_size: 点大小 1-9 visible: 是否可见 label_visible: 是否显示标签

设置动画——让滑块控制的机构动起来。

Args: label: 滑块标签, 如 "α" animate: 是否启动动画 speed: 速度 (0.1-10)

获取当前构造中所有对象的名称列表。

Create a complete mechanism: new construction → commands → styles → save .ggb + PNG. Use geogebra_batch for commands instead of this tool unless you need one-step save.

── MECHANISM TEMPLATES ──

Crank-Rocker (曲柄摇杆): O1=(0,0) O2=(d,0) α=angle° crank_len=r coupler_len=L rocker_len=R A = O1 + (rcos(α), rsin(α)) c1 = Circle(A, L) c2 = Circle(O2, R) B = Intersect(c1, c2, 1) Segment(O1, A) Segment(A, B) Segment(B, O2) Animate: StartAnimation(α) Style: thick segments, colored points

Slider-Crank (曲柄滑块): O=(0,0) α=angle° r=crank L=coupler A = O + (rcos(α), rsin(α)) c = Circle(A, L) guide = Line((0,-r), (10,-r)) B = Intersect(c, guide, 1) Segment(O, A) Segment(A, B) Circle(B, 0.1) Animate: StartAnimation(α)

Double-Crank / Drag-Link: O1=(0,0) O2=(d,0) α=angle° r1,r2=crank lengths L=coupler A = O1 + (r1cos(α), r1sin(α)) B = O2 + (r2cos(α+offset), r2sin(α+offset)) Segment(O1,A) Segment(A,B) Segment(B,O2) Animate: StartAnimation(α)

Four-Bar Linkage (general): Same as crank-rocker but adjust lengths. Valid if shortest+longest ≤ sum of other two.

── design_json FORMAT ── { "perspective": "G", "animate": "α", "speed": 0.5, "commands": ["O1=(0,0)", "O2=(6,0)", "α=45°", ...], "styles": [ {"label": "A", "color": [1,0,0], "point_size": 5}, {"label": "Segment(O1,A)", "thickness": 5}, {"label": "O1", "point_size": 6, "color": [0,0,0]} ] }

── WORKFLOW ──

1. New construction (automatic)

2. Execute commands in order

3. Apply styles (colors, thickness, point sizes)

4. Start animation on the angle slider

5. Auto-zoom and save .ggb + .png

Args: name: Mechanism name (used for filename) design_json: JSON string with design (see format above) output_dir: Output directory (default: current working directory)

Create a construction from a structured design dict. Preferred over geogebra_draw_mechanism for AI clients — no JSON string wrapping needed.

design dict format: {"perspective":"G", "animate":"α", "speed":0.5, "commands":["O1=(0,0)","O2=(6,0)","α=45°",...], "styles":[{"label":"A","color":[1,0,0],"point_size":5},...]}

Auto-behavior (no manual steps needed):

• Auxiliary circles named c1, c2, c3... are automatically hidden.

• The animation slider is auto-made visible and set to play.

• Construction must use 'c1', 'c2' etc. for circles to be auto-hidden.

Args: name: Output filename stem design: Dict with perspective, commands, styles, animate, and speed output_dir: Output directory (default: cwd)