Kinematics of pantograph device

AI Thread Summary
The discussion focuses on obtaining the forward and inverse kinematics of a pantograph device, which is characterized as a 2DOF planar elbow mechanism. The challenge arises from the need to combine two symmetrical planar elbow mechanisms due to the closed-loop nature of the pantograph. The key to solving this problem lies in understanding that each cell of the pantograph forms a rhombus, with perpendicular diagonals that create right triangles. The motors control joints Q1 and Q3, while Q2 and Q4 adjust accordingly. A clear approach to the kinematics involves leveraging the geometric properties of the rhombus and the relationships between the joints.
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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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