Figure 1<\/span><\/p>\n 3 Gimbals for Yaw, Pitch, and Roll<\/p>\n Source: <\/span>Wikimedia Commons<\/span><\/i><\/p>\n \u00a0 \u00a0 To understand what gimbal lock is, you will need to know what a gimbal is. A gimbal is a ring that allows an object to rotate in a specific axis. In three-dimensional spaces, you need three nested gimbals to allow full rotation in all axes, referred to as XYZ, or, in rotation terms, roll, pitch, and yaw respectively. This system is often represented as Euler angles, which describe a rotation as a sequence of angular movements on all axes.<\/span><\/p>\n \u00a0 \u00a0 Gimbal lock occurs when two of these three axes become aligned, reducing the degrees of freedom by one to two. As a result of this, the system loses its ability to independently rotate on one axis, leading to constraints in movement or unintended behavior. For instance, in space-faring vehicles, gimbal lock can prevent it from being oriented carefully, which could potentially jeopardize a mission.<\/span><\/p>\n Figure 2<\/span><\/p>\n Example of gimbal lock where the red and green axes have aligned<\/span><\/p>\n While gimbal lock seems like a trivial problem, it affects everyday things.<\/span><\/p>\n Figure 3<\/span><\/p>\n 3 axis robotic arm that utilizes rotations to move to any point in the 3D space surrounding it<\/span><\/p>\n Source: <\/span>KUKA Roboter GmbH<\/span><\/i><\/p>\n \u00a0 \u00a0 The cause of a gimbal lock lies in the representation of a rotation. When two gimbal axes align (when the angle between them is plus-minus 90 degrees), a degree of rotational freedom is lost. At this point, the system can not be distinguished between different rotations, leading to a lack of control. This is due to Euler angles being non-unique at certain points, known as a \u201ccoordinate singularity\u201d.<\/span><\/p>\n To counter these issues, various solutions have been created:<\/span><\/p>\n <\/p>\n Figure 4<\/span><\/p>\n A visualization of how positioning using a quaternion functions<\/span><\/p>\n Source: <\/span>Cmglee<\/span><\/i><\/p>\n \u00a0 \u00a0 Gimbal lock may seem to be just<\/em> a technical problem, but its impact reaches beyond specialized fields into the daily realm. From gaming and smartphones to robotics and aerospace, addressing gimbal lock ensures the reliability and accuracy of systems we rely on. Through the use of innovations like quaternions and alternative rotational models, engineers and developers can mitigate this hidden challenge.<\/span><\/p>\n <\/p>\n References and Sources:<\/span><\/p>\n Xsens Knowledge base<\/span><\/i>. (n.d.). <\/span>https:\/\/base.movella.com\/s\/article\/Understanding-Gimbal-Lock-and-how-to-prevent-it?language=en_US<\/span><\/a><\/p>\n Gimbal Lock | Paul Neale<\/span><\/i>. (n.d.). <\/span>https:\/\/paulneale.com\/gimbal-lock\/<\/span><\/a><\/p>\n Jackdevs. (2019, May 25). <\/span>Quaternions & Gimbal Lock<\/span><\/i>. Jackminnet. <\/span>https:\/\/jackmin.home.blog\/2019\/05\/25\/quaternions-gimbal-lock\/<\/span><\/a><\/p>\n![\"Gimbal](\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/5\/5a\/Gimbal_3_axes_rotation.gif\")
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Source: <\/span>MathsPoetry<\/span><\/i><\/p>\n\n
![\"Two](\"https:\/\/www.solidsmack.com\/wp-content\/uploads\/2017\/11\/kuka-musical-arms.jpg\")
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![\"Visualization](\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/0\/04\/Cayley_Q8_quaternion_multiplication_graph.svg\/2048px-Cayley_Q8_quaternion_multiplication_graph.svg.png\")
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