Sim4RAD: A MATLAB Toolkit for Design-Phase Sizing, Actuator Selection and URDF-Model Verification of Serial Robotic Arms

Jingchen Li

cs.ROOct 13, 2026

Sim4RAD: A MATLAB Toolkit for Design-Phase Sizing, Actuator Selection and URDF-Model Verification of Serial Robotic Arms

Authors: Jingchen Li

Organizations: Tencent Robotics X Lab (affiliation when this work was conducted)

Abstract

Actuator sizing is an early and consequential decision: joint torque and velocity specifications fix the motors, gearboxes and brakes before any CAD model exists. Sim4RAD is a MATLAB toolkit for that phase and for the verification that follows it. It builds a rigid-body model from a handful of parameters, and four analyses supply the specification: a static analysis combining lever-arm sampling with a posture search, giving a rated torque at a chosen payload envelope and a reproducible peak torque; a dynamics pipeline that reshapes a trajectory under one of four constraints, including the actuator torque-speed envelope; a stochastic analysis over many random motions, so a specification rests on a class of motions, not one trajectory; and a workspace and dexterity analysis that separates where the arm can reach from how it can reach there. Replacing the synthesized model by a URDF file turns the same analyses to verification. A 7-DOF anthropomorphic arm is compared in three layouts differing in the shoulder axis order and in whether the last wrist joint is coaxial with the payload. The static demand at half arm length is nearly the same in all three, and it sizes the joints rather than the sampled motion; reordering the shoulder axes leaves the worst-case torque unchanged at 55 N m and the reachable volume within 8 percent. A last wrist joint coaxial with the payload removes its gravity torque, reduces the adjacent wrist joint by almost a third and cuts the last joint demand tenfold in a 5 m/s scan, at the price of dexterity (mean 0.570 to 0.348). The same arm needs 20 to 37 times more torque for a 5 m/s target than for a 2 s motion: the scenario, not the trajectory, must be fixed first. Verification should use the URDF model of the detailed design; the toolkit is available at https://github.com/LasterLi/Sim4RAD.

Figures & tables

Figure 1: The four steps of the arm design flow and the role of the toolkit. The shaded steps are implemented in Sim4RAD: scheme simulation and optimization, which works on a synthesized model because no CAD model exists yet, and verification, which works on the URDF model exported from the detailed design. The dashed arrow indicates that a failed requirement sends the design back to the detailed-design step.

File	Content
config_modeling.yaml	gravity direction, model source (manual or URDF),
	joint limits, end load, sampling count
config_manual_robot.yaml	DOF, link/joint frames, link radii, estimated mass
config_dynamics.yaml	time step, planning space, interpolation, trajectory
	definition, constraint mode, actuator parameters
config_stochastic_dynamics.yaml	number of stochastic trajectories, parallelism

Table 1: Configuration files and their role.

Figure 2: The three layouts at the home configuration (arm hanging down, all joint angles zero); they are labelled Design 1–3 in the figure. All three have the same link lengths, the same shoulder offset and the same end load; they differ in the order of the first two shoulder axes (layout B) and in the orientation of the last wrist axis relative to the payload (layout C, where the last axis and the load offset are collinear).

	A	B	C
Link 1	$[0,0,0,-90,0,0]$	$[0,0,0,0,90,0]$	as A
Link 2	$[0,0,0.1,0,90,0]$	$[0,0.1,0,-90,0,0]$	as A
Link 3	$[0,0,0,-90,0,0]$	$[0,0,0,0,90,0]$	as A
Link 4	$[0,0,0.3,0,-90,0]$	$[0,0,0.3,0,-90,0]$	as A
Link 5	$[0,0,0,0,90,0]$	$[0,0,0,0,90,0]$	as A
Link 6	$[0,0,0.3,0,-90,0]$	$[0,0,0.3,0,-90,0]$	as A

Table 2: The three kinematic layouts. Frames are relative to the parent frame as

[x,y,z,\phi,\theta,\psi]

in m and degrees; limits in degrees. Layout C shares the first six link frames of layout A.

Layout	Requirement	J1	J2	J3	J4	J5	J6	J7
A	half-arm	36.66	38.14	23.44	23.86	4.89	4.88	4.90
A	full range	54.95	54.85	23.79	23.95	4.89	4.90	4.90
B	half-arm	39.59	36.55	23.15	23.83	4.90	4.89	4.90
B	full range	57.14	55.02	23.79	23.90	4.90	4.90	4.90
C	half-arm	36.46	38.48	23.62	23.95	3.44	4.90	0.00
C	full range	54.97	54.99	23.92	23.95	3.44	4.90	0.00

Table 3: Static torque demand with a 5 kg payload, in

\mathrm{N\,m}

. “Half-arm” is the maximum over sampled postures whose end-point horizontal distance is at most 0.4 m; “full range” is the maximum over all sampled postures. Sampling: 50000 configurations, uniform in the joint box.

Layout	J1	J2	J3	J4	J5	J6	J7
A	55.14	55.14	23.96	23.96	4.90	4.90	4.90
B	55.14	55.14	23.96	23.96	4.90	4.90	4.90
C	55.14	55.14	23.96	23.96	3.46	4.90	0.00

Table 4: Worst-case static torque per joint from the exhaustive search over postures built from multiples of

90^{\circ}

and the joint limits, in

\mathrm{N\,m}

. Layouts A and B give identical worst cases; only the wrist differs in layout C.

Figure 3: Static torque against the horizontal lever arm of the end point, layout A. Light clouds: individual random postures, one colour per joint (1000 of the 20000 samples are drawn, for legibility). Solid lines with markers: the maximum torque per joint within bins that hold an equal number of samples, i.e. the running requirement that defines the rated torque at a given payload envelope. The dashed line marks the half-arm-length envelope of 0.4 m used in Table 3 . $J1$ and $J2$ grow with extension, $J3$ peaks and then declines, and the remaining joints are insensitive to extension. J5–J7 coincide at about 4.9 $\mathrm{N\,m}$ .

Figure 4: Joint torque demand of the three layouts under three scenarios. Within each group of bars, from left to right: the half-arm-length requirement at a 5 kg payload, the worst case of the exhaustive posture search, and the maximum torque of the shared 2 s commanded motion of Section 5.4 . The joint index is the physical joint of each layout, so that layouts A and B differ in the assignment of J1 and J2. Values are recomputed by the plotting script.

Functional joint	A	B	C	A: gravity	A: inertia
Shoulder pitch	9.67	13.34	11.99	20.66	2.46
Shoulder lateral	18.82	14.41	20.54
Shoulder yaw	11.77	12.87	12.10
Elbow pitch	8.29	9.96	7.16
Elbow roll	1.99	2.36	0.57
Wrist pitch	1.10	1.58	1.55

Table 5: Maximum torque per functional joint over the shared 2 s commanded motion, in

\mathrm{N\,m}

. The last two columns report, for layout A, the maximum gravity torque over all joints (identical trajectory with velocities and accelerations set to zero) and the maximum inertial torque; their maxima occur at different instants and therefore do not add up to the combined maximum of the A column.

Joint	A	B	C	Limit
1	404.61	426.72	403.73	135
2	628.01	587.70	702.74	135
3	315.25	205.62	294.14	67.5
4	263.38	329.96	308.41	82.8
5	56.89	59.18	46.27	82.8
6	65.70	56.91	78.43	41.4

Table 6: Torque demand at the 97.72th percentile of random motions whose displacement exceeds 0.2 m, with each motion rescaled to a 5 m/s end-effector peak, in

\mathrm{N\,m}

. The last column is the peak torque of the reference joint modules.

Joint	A	B	C	Limit
1	200.95	162.62	203.38	90
2	113.29	141.92	121.80	90
3	210.75	192.72	213.22	90
4	122.51	126.85	103.42	180
5	219.89	344.22	264.70	180
6	88.73	91.73	116.40	360

Table 7: Joint speed demand at the 97.72th percentile under the same 5 m/s scans, in rpm. The last column is the peak speed of the reference joint modules.

Figure 5: Stochastic torque requirement of layout A: one panel per joint, with the maximum torque of each random motion against the displacement of that motion, the mean and standard deviation per distance interval, and the peak capability of the corresponding reference module as a dashed line. All joints are above their capability at this end-effector speed.

Reachable positions	246	265	245
	A	B	C
Reachable volume (m 3 )	0.830	0.894	0.827
Mean dexterity	0.570	0.594	0.348
Maximum dexterity	1.000	1.000	0.667
Positions with dexterity $\geq 0.5$	68 %	73 %	21 %

Table 8: Workspace of the three layouts: reachable positions of the grid, reachable volume estimated by one voxel per position, and dexterity statistics. Dexterity is the fraction of the 12 sampled approach directions that admit a collision-free solution at a position.

Panel of Figure 6 — Figure 6: Reachable workspace of layout A (left) and layout C (right), coloured by dexterity. The two layouts reach essentially the same volume, but layout C admits far fewer approach directions at most positions.

	A	B	C
Difference from A	—	shoulder order swapped	last joint coaxial
Static half-arm ( $\mathrm{N\,m}$ )	36.7 / 38.1 / 23.4 / 23.9 / 4.9 / 4.9 / 4.9	39.6 / 36.6 / 23.2 / 23.8 / 4.9 / 4.9 / 4.9	36.5 / 38.5 / 23.6 / 24.0 / 3.4 / 4.9 / 0
Static worst case ( $\mathrm{N\,m}$ )	55.1 / 55.1 / 24.0 / 24.0 / 4.9 / 4.9 / 4.9	same as A	55.1 / 55.1 / 24.0 / 24.0 / 3.5 / 4.9 / 0
2 s motion, max ( $\mathrm{N\,m}$ )	18.8	14.4	20.5
5 m/s scan, J2 ( $\mathrm{N\,m}$ )	628.0	587.7	702.7
5 m/s scan, J7 ( $\mathrm{N\,m}$ )	58.3	70.6	6.3

Table 9: The three layouts side by side. Torque vectors are given for joints J1–J7 in

\mathrm{N\,m}

. “Static half-arm” and “static worst case” are the two static sweeps; “2 s motion” is the shared commanded motion of Section 5.4 ; “5 m/s scan, J7” is the 97.72th percentile of the stochastic scan.

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