How can I fix the following problem?
The second bone most move from left to right and v.s. wen the first bone changed in angle. The tail of the third bone most be a fix position.
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If you want a fixed joint, you need a bone head in that position. Once you have setted the two joint bones, you can achieve the desired behaviour with constraints: IK, track to, stretch to, depending on the desired movements.
In my example a simple 2 bones IK chain targets toward the IK target bone, which will be extruded from the "fixed head" bone and setted as not deforming (uncheck its "deform" option).