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For each joint relation you model, you would get one homogeneous transformation matrix (HTM) T $$T^{i-1}_i$$ If you multiply all HTM from base to end-effector, you would get what is called forward kinematic matrix FK $$FK(\theta) = T^0_N= T^0_1*T^1_2*...*T^{N-1}_N$$ which map joint configuration into cartesian space (represent pose of end-effector). Then for ...

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