Learning general-purpose models from diverse datasets has achieved great success in machine learning. In robotics, however, existing methods in multi-task learning are typically constrained to a single robot and workspace, while recent work such as RT-X requires a non-trivial action normalization procedure to manually bridge the gap between different action spaces in diverse environments. In this paper, we propose the visual kinematics chain as a precise and universal representation of quasi-static actions for robot learning over diverse environments, which requires no manual adjustment since the visual kinematic chains can be automatically obtained from the robot's model and camera parameters. We propose the Visual Kinematics Transformer (VKT), a convolution-free architecture that supports an arbitrary number of camera viewpoints, and that is trained with a single objective of forecasting kinematic structures through optimal point-set matching. We demonstrate the superior performance of VKT over BC transformers as a general agent on Calvin, RLBench, Open-X, and real robot manipulation tasks. Video demonstrations can be found at https://mlzxy.github.io/visual-kinetic-chain.