Kinematics of pantograph device

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SUMMARY

The discussion focuses on obtaining the forward and inverse kinematics of a pantograph device, which is characterized as a closed-loop mechanism composed of two planar elbow mechanisms. The symmetry of the pantograph complicates the kinematic analysis, as it requires the integration of both sides of the device. Key insights include the importance of the rhombus shape formed by each cell, where the diagonals are perpendicular, facilitating the use of right triangles in calculations.

PREREQUISITES
  • Understanding of 2DOF planar elbow mechanisms
  • Knowledge of kinematic analysis techniques
  • Familiarity with closed-loop mechanisms
  • Basic geometry, particularly properties of rhombuses and right triangles
NEXT STEPS
  • Research methods for solving forward kinematics in closed-loop mechanisms
  • Study inverse kinematics techniques specific to planar robotic arms
  • Explore the application of geometric properties in kinematic analysis
  • Learn about simulation tools for modeling pantograph mechanisms
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Mechanical engineers, robotics researchers, and students studying kinematics who are interested in the design and analysis of pantograph devices.

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I need to obtain the forward and inverse kinematics of a pantograph device. It is easy when only the one side of the pantograph is considered; So, it becomes a 2DOF planar elbow mechanism, which is easy to solve. However, there is symmetry on pantograph, so I kinda need to combine two planar elbow mechanism, but it confuses me since it's a closed loop mechanism.

This is the depiction of the mechanism;
http://i.imgur.com/M3ANKre.png

Q1 and Q3 are controlled with the motors and Q2 and Q4 rotates accordingly.
How am I supposed to approach this mechanism ?
 
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The key to a pantograph is that each cell forms a rhombus, and the diagonals of a rhombus are always perpendicular. So you are dealing with right triangles.

Chet
 

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