fixed gradio version

README.md

@@ -23,7 +23,6 @@ license: mit
 pinned: true
 short_description: Interactive 2-DOF robotic arm simulator with real-time inver
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 SEO: Interactive Arm Simulator, 2-DOF robotic arm, inverse kinematics, python gradio app, robotics education, interactive simulation, arm kinematics visualization, open source robotics tool, robot arm math, educational robotics, engineering demo, real-time robotics, STEM learning
 Description: Interactive Arm Simulator is a Python Gradio app for simulating and visualizing the inverse kinematics of a 2-DOF robotic arm. Adjust controls, see real-time results, and learn the math behind robotic arms. Perfect for education, demos, and open source robotics projects.
@@ -75,24 +74,17 @@ This app calculates the joint angles needed for a 2-link arm to reach a target p
 
 **1. Elbow Angle ($q_2$):**
 Uses the Law of Cosines:
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 $$ \cos(q_2) = \frac{x^2 + y^2 - L_1^2 - L_2^2}{2L_1L_2} $$
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 **2. Shoulder Angle ($q_1$):**
 Combines the angle to the target and the triangle's internal angle:
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 $$ q_1 = \alpha - \beta $$
 Where:
 - $\alpha = \text{atan2}(y, x)$ (angle to target)
 - $\beta = \text{atan2}(L_2 \sin(q_2), L_1 + L_2 \cos(q_2))$
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 If the target is unreachable, the app shows a warning and marks it in red.
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 ## 📝 Copy the Core Python Function
 The app includes a dropdown with the following code for your use:
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 ```python
 def inver_k(l1, l2, x, y):
     """
@@ -116,7 +108,6 @@ def inver_k(l1, l2, x, y):
     q1 = alpha - beta
     return (True, q1, q2)
 ```
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 ## 📚 Credits