What is the difference between a twisting joint and a revolving joint in Groover's notation?

Both rotate. In a twisting joint (T) the axis of rotation is parallel to the axes of both the input and the output link, so the output link stays in line with the axis and spins about it. In a revolving joint (V) the axis of rotation is parallel to the input link only, and the output link comes off perpendicular to that axis, so it swings around it like a boom.

What does the notation TRR:TRT mean?

Read left to right from the base. TRR is the body and arm: a twisting base joint, then a rotational shoulder, then a rotational elbow, which is the articulated or jointed-arm configuration. The colon separates the wrist. TRT is a three degree of freedom wrist: roll, pitch, roll. Total is six degrees of freedom.

Which Groover joints are prismatic and which are revolute?

Linear (L) and orthogonal (O) joints are translational, so both correspond to prismatic joints in P and R notation. Rotational (R), twisting (T) and revolving (V) joints are all rotary, so all three correspond to revolute joints. This is why Groover's notation carries more information than the P and R string.

Groover's Joint Notation Visualizer — L, O, R, T, V Joints & Robot Configurations | Piyush Wairale

GATE Robotics & Automation · CIM · Robot anatomy

Five letters describe every
industrial arm. Here is how.

Groover classifies robot joints not by whether they slide or turn, but by how the axis of motion sits relative to the two links it connects. Get that relationship straight and the whole notation falls out — L, O, R, T, V, read left to right from the base, with a colon before the wrist. Below: each joint moving, then a decoder that builds the arm from whatever string you give it.

L · O · R · T · V Body-and-arm : wrist Piyush Wairale · M.Tech, IIT Madras

Part one

The five joint types

Two of them translate, three of them rotate. What separates each pair is the geometry: which link is parallel to the axis of motion, and which is perpendicular to it. Drive the slider and watch what stays fixed.

Joint variable

Input link Output link Axis of motion

Part two

The decoder

Type a string, or pick a standard configuration. Each letter adds one joint to the chain, base first. The colon marks where the arm ends and the wrist begins.

Notation string

Standard configurations

Reads as

3Arm DOF

3Wrist DOF

6Total DOF

Joint by joint, base to tool

Part three

Reference

The three tables an exam question is built from: the joint types, the five body-and-arm configurations, and the wrist.

Table 1 — The five joint types. "Input link" is the one nearer the base; "output link" is the one nearer the tool.
Sym	Name	Motion	Axis relationship	P/R	Where you meet it

Table 2 — Body-and-arm configurations. The P/R column shows why Groover's letters carry more information: cylindrical and Cartesian both read PPP-like in places, and spherical and SCARA share RRP outright.
Sym	Configuration	P/R	Read as	Work envelope

Table 3 — Wrist assemblies. Roll turns about the arm axis, so it is a twisting joint; pitch and yaw both swing across it, so both are rotational joints.
DOF	Notation	Motions	Notes

Part four

Check yourself

Eight questions on the notation, in the form GATE and PSU papers ask them.

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